Both of these sentences refer to a statement you made in the past.
I warned them not to cross the river
This means exactly what it says: You said to them "Don't cross the river.".
The second sentence isn't quite right, but it seems like a forgotten word typo rather than actual incorrect grammar, so I'll answer as if it was correct. If you did mean the sentence to be exactly as it is above, then it is incorrect because there is no direct object
I warned them about crossing the river
The difference is that you just told them something about crossing the river would be bad, you did not tell them not to do it (although you could have strongly implied not to do it)
For example, if you said "Be careful crossing the river - there is a strong current that could suck you underwater!" and they drowned you could later say "I warned them about crossing the river."
A sentence that strongly implies that they should not cross without actually saying "Don't cross the river" would be "If you try to cross the river, you will die."