new to hunting with a Air rifle for rabbits and squirrels small game need help

Well I suck at offhand shots and generally wont take one unless its 5 or 10 yards. And then only a maybe. I always try and find a rest of some kind to support my gun and left hand. Generally where I hunt there is always something close by to use, such as trees, railings, fence posts etc. 

I tried using a bipod but it doesn't work for me. Makes the gun unneccessary heavy to carry and I never seem to find the right spot to set it as I'm always on the move. 
 
I have a trigger stick and love it, but I don't like carrying it when squirrel hunting. For groundhogs, I use a cheap bipod mounted to the gun. Its not an expensive one, but it does the trick for prone shots in fields at farther distances. For squirrels I rest the gun against the side of a tree if I am standing or my knee or side of my leg if seated. Anything is better than nothing in my opinion. Kill zones on squirrels are mighty small. Try some methods out at the range to see what works for you and then practice that way, is the best advice I can give you. Happy hunting!
 
All depends. I do a lot of squirrel hunting with my air rifles. If I am able to, I will always use the side of a tree to steady my shot. If I'm in a situation that a shot presents itself and I don't have that luxury, I will shoot off hand or drop to a kneeling position preferably. That way I have more support . Off hand takes much practice to be proficient with.
 
I have a trigger stick and love it, but I don't like carrying it when squirrel hunting. For groundhogs, I use a cheap bipod mounted to the gun. Its not an expensive one, but it does the trick for prone shots in fields at farther distances. For squirrels I rest the gun against the side of a tree if I am standing or my knee or side of my leg if seated. Anything is better than nothing in my opinion. Kill zones on squirrels are mighty small. Try some methods out at the range to see what works for you and then practice that way, is the best advice I can give you. Happy hunting!

This would be my post exactly. The Trigger stick is great. I have a bipod tall. Makes a good walking stick too. But it can get in the way and makes noise in the woods/brush. A good tree seems to be the best for me. Anything, birds, squirrels or rabbits are no problem under 35 yards free-hand. But I shoot a couple hundred times a day. That’s how I spend my lunch hour. 
 
When I was a boy it never occurred to me to use any type of a rest while hunting small game so every shot I took was offhand, that's what yuh did back then. But I shot my air rifles nearly every day because that's what was the most fun to me at the time.

So I say to practice offhand and kneeling regularly until you can confidently put a pellet in the center of the chest most of the time out to 30 yards.

I rarely hunt anymore but this last year I shot one Jackrabbit in the head at 40Y offhand, I couldn't get closer nor could I lean on anything so I waited til the crosshair was just right. Then shot two ground squirrels both center chest 30Y offhand. I guess the confidence comes from all the memories of doing the same thing in my youth??? and well I shoot offhand almost weekly with rimfires and centerfires.

No shame in using aids either. Wish I knew then what I know now when it comes to that. 
 
I hunt thick woods and brush for rabbit and squirrel.

As stated the killzone is small.in .22,.25 and .357 I aim for head shots.

Most times it's free aiming but if I'm not spotted by the prey I try to rest on a branch or tree.Free aim not rested I try to stay withing 30-40 yards.Rested I stretch out to 80 yards.On a bipod in a feild I stretch to 100 plus.Providing I'm using an accurate gun and ammo.My personal rule is If I can not hit a 1" target at 100 yards that day I do not make long range shots.Im not trying to wound an animal.Although the .357 will destroy rabbit and squirrel almost no matter where it gets hit in the head/face or neck area.
 
My advice. Shoot for the heart/lungs. The killzone is much larger for chest shots. After my 3rd or 4th bad head shot on squirrels (and I'm a pretty good shot and a conservative shooter) I moved to the "boiler room" and my shot to humane kill ratio has gone up by at least an order of magnitude. I now only consider head shots from steady rests...something equivalent to a target shooting rest with a two point balance.

In case you think a head shot is more "humane" consider the ratio of projectile size of a pellet to a squirrel, vs. a slug to a deer and you will realize even .177 pellets can be very effective comparatively. I've dropped squirrels very quickly with decent expanding .177 pellets placed in the boiler room.


 
I started using primos trigger sticks this year. I just work my way to active ( cutting/feeding) hickories. I set up and wait. 
I’m not after limits anymore. So, I wait for headshots. If I’m moving slowly from one vantage point to another I always try to stop at a tree with a rest. If area looks good I’ll unfold the stick. I have it slung around my back. 


I will take close shots off-hand if no other choice, 10-20 yards.

I’d much rather hold my shot than take an iffy shot.
 
I'll add my two here but it will just be a repeat of what others have said. First the KZ on a gray squirrel chest shot is about the size of a US quarter, so maybe an inch on a big gray. The size of the KZ on a head shot for the same animal is about the size of a dime, so maybe 3/4" on a big squirrel. Rabbit head shots on cotton tails are about the size of a quarter and chest shots are about the size of a silver dollar. 

I have not taken a body shot in a long time. I, personally just never had much luck with them, but I do believe that is because I was shooting too far back behind the shoulder. If you are going to take body shots on squirrels, keep in mind the KZ is bounded at the bottom by his elbows and at the top by the base of the neck and shoot as if to break his front shoulders. You will probably have better luck than I did when I was messing up body shots. A guy on youtube called the "Carolina Bean Shooter Man" who hunted rabbits with a slingshot once said, "Why, a rabbit is the easiest thing there is to kill with a bean shooter!" He was right. Body shots on rabbits work a treat but you certainly can head shoot them.

Don't push your range. You know what size the KZ you want to shoot is. Figure out how far you can hit that size spot every time (because adrenaline 😁 even with bunnies) and limit yourself to that range or closer. Just don't take shots longer than that. Learn to stalk a bit instead. Know your rifle. Check your zero before you go into the woods.

You will enjoy this sport and the meals it can provide. Good luck.
 
I have a Primos Trigger stick for stalking. But if I can, I use the Caldwell Deadshot. The heavier duty one. It’s by far the steadiest and easily moveable. I use that when moving to spots to shoot from, which is mostly what I do. Close up I do the head shots but 85 yards or so I get into the center of chest shots. You’re gonna have some real fun!
 
I tried to head shot a rabbit at 65 yards with my .357.

I have several times before without issue.Either I pulled the shot or had a flier.Im pellet struck it in the joint of the jaw.When I walked up the bunny was dead.The larger caliber enlarged the killzone I suppose.Its complete skull was shattered from that impact.At 65 yards my pellet was still retaining about 145ft lbs of energy.A poor shot indeed but a large caliber covered my mistake.