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The two main things are to only install mature applications that have a track record of significant installs and lots of reviews, and check out the developer to see what else they have done and whether there are complaints about their other apps. This is far from perfect, but it can help avoid a lot of problems.
The anti-virus programs on Android phones are mostly a waste of time, but some of them can alert you to apps that are hiding malware. Sometimes anyway. They can also give you false positives.
One piece of advice that I've always found useless is to review the apps permissions. Well, good luck getting many apps that actually respect your privacy. Plus, just to function many apps need permissions for access to things that aren't apparent at first glance. Yeah, in an ideal world I would only install apps that didn't request any permissions, but until we pay for every app and don't expect developers to make us stuff for free, there is going to be a trade off.