Pick a rifle that fits you. Length and weight are important. You should be able to comfortably hold it steady at ninety degrees to your body (parallel to the floor) without having to rest it on anything.
One method of sighting at home is to bore-sight it. For this you will need a break barrel air rifle. If you do not have one then skip this step. Break the barrel just a bit so you can see down the barrel. Look down it and aim at a target. WARNING: Do not look down from the end of the barrel as it can risk eye injury. once you have picked and aimed at a safe target through the barrel look through the sights and line them up with the same thing while keeping the barrel aimed at the target.
Tuck the stock into your right shoulder, where it feels comfortable. This applies even if you are left-handed; most rifles are shaped for right-handed users. If you are left-handed and find this uncomfortable, you can buy left-handed rifles.
Place your dominant hand on the grip. Keep your finger off the trigger for now.
Note the distance from your shoulder to the grip. Your other hand should be about the same distance forward, under the body of the rifle. Don't touch the barrel.
Instead of moving your eye down to the rifle, hold the rifle across your body so that you are standing side-on to the target. This allows you to look along the barrel by simply tilting your head slightly, and is much more comfortable.
Sight on your target. Check your rifle's instructions to learn how to use its particular sight. Most often, you have a small, notched piece of metal at the end nearest you, and a vertical stick (sometimes within a ring) on the end of the barrel. With this type of sight, you have to line the rifle up so that your target point is in the centre of the notch, and then bring the barrel up so the stick fills the notch, with the top of the stick level with the top of the notch. On quite a bit of new rifles you will have two red dots on the side nearest you and a green dot on the end of the barrel. Repeat the last steps the same way. Remember: Back sight, front sight, target.
Use BRA: Breathe, rest, aim method. Take a deep breath, let it out halfway and hold it, rest a second and then slowly squeeze the trigger. To avoid trigger flinch you should squeeze so slowly but steadily that the firing surprises you. If you are not surprised then you knew it was coming because you squeezed too hard and possibly reflexively flinched which throws off accuracy.
Note where the shot landed. No sight will be perfect, so adjust. If it landed too high, aim a little lower. If it hit over to the right, aim left.