I can totally relate to your personal goal. When I first started working out with my personal trainer, I wasn't able to do a single regular push-up, sit-up, or chin-up. Rather embarrassing as a guy.

If you have access to weights or weight machines, I'd recommend using them to develop more muscle mass and tone up what muscles you do have. If you don't have access to weight lifting equipment, there are some plank poses that will help.
Two that most resemble regular push-ups are:
1.) Position yourself in a regular push-up position with arms fully extended. Keep your body rigid and hold the position for as long as possible.
2.) Same as the first but instead of supporting your weight on your hands, lower yourself onto your forearms and hold the position for as long as possible.
Keep working on it, I know you'll get there.