Quarry

Brown Rats
Most air gunners' favourite quarry. Ugly, evil and disease spreading, the rat can (and does) live virtually anywhere. Their favourite homes are places such as pig and chicken farms (the older ones with overgrown ditches and so on, and not too much concrete) where ratty makes a very good living off spilled food, bedding and animal dung, but huge colonies also exist covertly in towns and cities. There are some 10 million rats in Britain at present, but despite their numbers, they are usually very timid, and extreme stealth needs to be exercised when hunting them. They are most active at night, but can also be seen scuttling about during the day, particularly on warm overcast evenings. They can be shot all year round, but come the colder winter months more of them will move into farms from the countryside, where their food supplies are dwindling and their lairs losing cover.

Probably the best way to locate rat colonies is by the mess they leave- droppings, spilled food and so on. Rat droppings are grey, torpedo shaped objects around 5mm long, and fresher ones are greyer and shinier. Once a colony is located (or simply when you have access to a good shoot) the next thing to decide is where you will shoot from. Rats are timid, but young ones are fairly stupid and the most basic hide will usually grant you a few kills. Evening and night hunting will usually produce best results (when rats have learned that fewer people will be around), but a few rats should be around at any quiet time, and more can be decoyed out. Mushy cat food is good for this- cheap and fairly convenient to carry around. The lack of chunks means that rats cannot carry the bait away to eat it, and must stay under your gun barrel. For a few days before a hunt it is often well worth baiting a patch of shoot, so that rats come to associate the area with a free feed. Lamping is good, particularly when combined with baiting. Rats are not "scared" of light, but they will be wary of it, so you will need to make the area attractive- go into the lit area and get food, or stay hungry in the dark... Failing this, an ambush can frequently be set up in some of the lighter areas on rats preferred travel routes (for example railings running past food bins). As ever, studying your quarries habits will help enormously.
A problem to be aware of with rats is Weils Disease (Leptospirosis). This is carried by bacteria that spread in rat urine. In rare cases it can be fatal, and its symptoms are broadly flu- like, with headaches, temperature, and joint and muscle pain. Do not handle dead rats- collect the corpses with a stick and burn them. If a rat bites you, or you have the above symptoms, see your doctor at once. (At lease for a tetanus jab).

Rabbits
Rabbits are one of nature's most prolifically breeding species. They are to be found almost anywhere, but they seem to particularly like exposed hillsides to "graze" on, and sandy soil to burrow in. I live in Kent, chalk grassland country, and rabbits are to be found almost anywhere. To find rabbits, search whatever land is available to you- usually, the signs will be obvious- patches of fur and rabbit droppings, huge holes and sometimes well worn paths between them. However, in brambly country rabbits can make very concealed burrows, and have their runs under the top layer of shrubs. These are harder to spot, but a stroll with a torch at night will usually reveal a few bunnies.
Rabbits are particularly wary from Autumn onwards. From late January onwards, most rabbits are breeding and should not really be shot. (You are only spoiling future sport). By March/April, you're likely to find pregnant does, or ones with young families, which again you will only spoil future quarry numbers by shooting. By June or July, however, most of the young rabbits have enough cunning to make a stalk challenging and enjoyable. The long, sunny evenings will let you stalk to plenty of targets, and the long grasses make concealment fairly easy (but easy for the rabbit too). As the evening passes, rabbits will move further and further from their burrows, and will hence move further out of range of cover. Ambushing the warren exits is good at this time, or in areas with sufficient cover, good stalking can be had. If you set out at around 5Pm, you can stalk your shoot, then finish up with an ambush (light allowing) as rabbits head back to their burrows during dusk and darkness. (The only thing is- you must be stealthy getting into ambush position, because if you scare the rabbits it could be an hour or more before they venture back out).
Rabbits are sensitive to weather, and try to feed around storms and similar. So, if you go hunting the night before storms are forecast in your area, you should be rewarded with more bunnies that usual. Head shots are the best, but heart shots can be attempted- see kill zone picture below. Hits in the blue will cause instant death, hits in the yellow death within a few seconds.

Crows
The most "evil" members of the corvid family. Ugly and unpleasant, with big strong beaks and sharp eyes, crows eat the eggs and chicks of songbirds and indeed anything smaller than themselves. They have phenomenal eyesight (they are capable of telling the difference between an unarmed man and a man with a rifle), and also an excellent sense of smell. The John Crow is reputed to be able to smell a dead lizard from approximately 1 mile away. Unsurprisingly, baiting crows in with dead rabbits and similar is a very good tactic, better if the rabbit is slit open as crows (and magpies) are partial to rabbit intestines and eyes. The rabbit should be firmly pegged out, and both crows and magpies should be shot swiftly, as removal of the eyes will render your bait less attractive to other birds. Road kills can be used for baiting, as long as they aren't too squashed.
A good hide is useful in conjunction with a bait. If no bait is available, your hide should be set up near a suitable tree- usually tall and old, and always with a few dead branches or other clear patches at the top (pine and other conifers are particularly popular). In these clear patches crow sentinels will sit and view the surrounding area, so you want to be in your hide before they arrive. If you don't do this, you will scare them off, and they will move to another tree, or maybe even a different area all together.

Magpies
Most of the points that apply to crows apply here also (they are both members of the corvid family), but magpies can be "called"- take a film canister, and half fill it with pellets. Tape the lid down, and when shaken, it will produce a "rattchakk" type of noise which with practice can be made very magpie-like. Try and get their call pattern- 6 short trills, interspersed with single longer trills.
Magpies if anything are more tempted by a rabbit decoy than crows, and they can also lured into range with a decoy owl. Place this on a fencepost or other area where owls are likely to be found, slip into your hide and wait. Magpies, Jays and various other birds will mob the "intruder" and try to drive it off. A flapping owl will work even better. However, be wary- other birds are keen to chase the owl away, and these (e.g. blackbirds) are not legal airgun quarry. Make sure you know what you are shooting!

Grey Squirrels
A handsome and difficult quarry. Squirrels are very sharp eyed, except in autumn when young squirrels can be quite dim. Tactics depend on your shoot- in areas where squirrels are unused to humans and do not appreciate their threat, you should have no trouble in bagging a few, particularly if you can find their preferred routes and feeding places. (Indicated by old nuts, broken twigs,ect). However, as the season advances and young squirrels learn, or if you shoot an area too frequently, they will wise up. Now some classic stalking can be employed. Camouflage is usually required, and faces and hands should be smeared with bars of camouflage paint. Full face netting and a camouflage cap are better still. (Squirrels associate the upturned pink moon of a face with danger, and will be nervous or just run away accordingly).
From their high vantage points, squirrels see almost everything. If cover is limited, getting in range will be a problem, but if you wait patiently and quietly, the squirrel may move within range, or at least move into an area where stalking is possible. If, however, the squirrel catches a glimpse of you, it will probably sprint to the nearest handy tree (if on the ground) and climb about 3M up the trunk. It will be alert, and if it spots you again, it will try and put the trunk of the tree between you and it, and climb up higher. If you have a friend with you, get him or her to attract the squirrel's attention on one side of the tree, and when it sidles to the other side of the tree, you can be waiting for it. However, if the squirrels are more nervous-natured, they will just sprint for the deepest cover and you will have a hell of a job winkling them out.

Wood pigeon
These birds are very tough, but not too observant. They like to rest and roost in thick trees, and spotting them is a tricky problem. All too often, you are only alerted to their presence when they fly off with a loud clatter of wings and a crashing of twigs. That said, once spotted, they are fairly easy to stalk as long as you are quiet and careful, and wearing face camo. If the bird you spot is asleep, you won't need to be so careful, but I don't really think that it's sporting to shoot sleeping birds. It's up to you. (Anyhow, be aware- the bird you are stalking may be surrounded by four or five other birds, one of whom is likely to see you as you are unaware of it. Off it goes, and the others hear the racket and follow it. Try and stalk birds that are definitely on their own, and also be aware that a wood pigeon with its head under its wing can look a lot like an old stump of branch).

A wood pigeons breast is armoured with thick feathers, and it will be further protected by a crop stuffed with grain or other food. (Wood pigeons can frequently be found in stubble fields, cleaning up the last of the years crop, or starting into next years). Only go for the chest if you are sure you can hit the heart- never underestimate the toughness of these birds (and crows). A pigeon shot through the lungs will probably die eventually anyway, but it is your duty as a hunter to kill it as cleanly as possible. If possible, aim for the base of the neck (or the back or side of the head itself), or failing this a shot through the shoulders with a big pellet (preferably hollow point or flat head) should put the bird straight down. The first shot often numbs the bird, and can make it impervious to further shots, so make the first one count. After death, woodies often twitch quite a lot. If you are not sure that they are totally dead, shoot them directly in the head or heart, or wring their neck.