As always, it depends what you want to achieve...
Recreational push ups or press ups, you can do every day.
If you want some results, see if you can develop some plan for yourself, usually you'd want to exercise the whole body and not just triceps. There are many styles and thousands plans online, it's pointless to keep repeating them. The best is to exercise opposite muscles in on day, for example:
Day 1 - Arms:
10 Push ups
5 Pull ups
.... Repeat 5 series. Exercising in series is much better than doing on exercise to exhaustion.
Day 2 - Legs:
10 Squats (quadriceps)
10 Leg curls
.... Repeat 5 series
Day 3 - Arms again
Day 4 - Legs again
.... This way your muscles get plenty of rest. There are of course many exercises and many variations you can add to it....
Similarly, you can do weights say 3x per week (Mo-We-Fr) and cardio 2x per week (Tu-Th).
If you want more serious results, focus on main exercises such as deadlift, overhead press or bench press, squats, rows, perhaps add some pull ups. Generally speaking, the heavier weight the more rest in between. For example, deadlift - you might get much better results when you lift heavy weights 1-2 per week vs intermediate weight 5-6 X per week... Squats and bench, you should be probably doing 3-4 times per week for optimal results, with at least one day of rest in between...
Check out program called 5x5, IMO it's pretty good, simple and efficient. If you put lots of hard work in it you will get amazing results in strength as well as muscle size...