If you do not have a staircase at home, you can use other sturdy objects such as a table or bed at comfortable gradients. Over time slowly increase the number of pushups. When you feel you have mastered that level, add one push up with your arms one step lower. Build up again. Eventually you may be doing floor pushups and feeling very proud of yourself.
Exercise causes muscles to contract.
Through stretching, you want your muscles to achieve a nice, elongated state. Never stretch cold muscles. Good places to stretch are first thing in the morning while under a warm comforter. Or better yet, in a hot shower, a sauna or hot tub, or after a hot bath. Exercise also warms up your muscles.