Getting strong by doing push ups...

I can barely do 3 push ups! im weak in the areas for push ups and I want to know what kinda of exercises should I do to build up to doing 10 reps and 3 sets of push ups? I have pretty strong biceps from caring 15 pounds everyday, but its my triceps and chest muscles getting weak. Also, what other exercises are good to gain muscle in thighs/butt? Or are there activities that are good and work all muscles?
Another question! I want to start running this spring, I ussaully just walk my dog, but I want to start jogging. How do I build myself up to that? I can run down the stop sign near my house till my heart is really pumpin which is about 89 yards. I know im not in my best shape.
Any help, thanks

squats are the only way to go for butt/thighs

and for arms, simply just do butterflies.

if you dont know what the workouts I just told you are, ask me

variation of squats, lunges, leg presses, running at an incline, olyptical machine, calf raises while squeezing buttocks, and deadlifts all work legs and buttocks.

It is good to work your entire body so you are balanced.

Try long distance, sprinting is great for the lungs and all but if you want lungs, then do suicides(sprinting back and forth 10-30yrds apart). Walk/Run for about an hour 3-5x a week and you'll build yourself up. Just keep track how far you go and try to improve a little every couple weeks.

with the push-ups you nneed to strengthen your upper arms, weight lifting can help that (start off small)
bicep curls
and tricep curls will also help you a lot for push-ups

to start small for your pushups instead of planting your feet, kneel it drops some weight on your pushups so you can get out more reps, after your muscles get used to the new movement they will be able to support more weight for longer time ie: they can do more standard pushups. and as far as theighs and but goes do split leg squats stand with both feet together then step out with one and kneel till your back knee is just above the floor then push back up to starting position and do the same with your other leg. after your used to this start holding dumbells when you do it. it will torch your theighs butt and abs.