In some cases you can use なんとかなる to say 'everything will be fine', but なんとかする might be better when you want to convey that you are really committed to improve the situation.
Literally なんとかなる means something like 'the situation will just take its course; things will go as they go'. It is in 3rd person, more neutral as such, and does not tell whether the speaker really does something.
For example, if you are talking about a work project that is stuck with some problem, you would better tell your supervisor なんとかします because なんとかなります would sound irresponsible or vague.
I think people (like me) tend to use なんとかなる more exactly because it does not put any responsibility on those who say this :). So the distinction is partly psychological, and using なんとかなる does not necessarily mean that the speaker will NOT do anything.
A note on the endings
The endings よ or さ do not affect the meaning.
- よ in 何とかなるよ indicates that the speaker particularly tries to make the listener be aware that it will be okay.
- 何とかなるさ sounds masculine
If uttered cheerfully, it sounds more optimistic and probably softer than なんとかなる. A possible English parallel is saying it with emphasis on 'will': "Things will be fine!"
FYI: なんとかなるわ is a feminine version and なんとかなるわよ is feminine + emphasis same as よ above.