The equipment you will need to complete this task is simple. Some different size needles, some thread and some scissors.
Choose a thread that matches the thread colour used on the other buttons or the colour of the material. White thread for white shirts, dark thread for dark jackets. Next cut a piece of thread about 18 inches long, approximately the length from your finger to elbow. Then thread the needle, feeding the eye through the eyehole. A tip here is to moisten the thread with your tongue before you try to thread it into a needle. This will stiffen it and make it easier to fit through the eyehole.
Your next step, after the thread is through the eyehole, is to move your needle to the middle of the thread and fold the thread in half. Tie a knot in the end of the thread ? a double knot is best to make it doubly secure. The thread should now be doubled and ready to sew.
Place the button on top of the material where you propose to sew it in place. You can place a match or similar between the button and the material to give it the necessary slack. From under the material, push the needle up through the material and one of the holes in your button. Buttons do come in different types, with two or four buttonholes or they can be attached with a single clasp underneath. Push all the way through until the knot is anchored against the material. Push your needle down through the next hole on the button and through the material. Repeat this last step three times going up and down through the hole in the button and through the material, so that each hole is properly secured by multiple strands. When your are happy that your button is strongly secured, end with the needle on the material side and secure it with a knot. Double knot the end and snip off any spare thread with some scissors.