What styles of beer pair well with white fish? I eat fish often, and as a beer lover, would like to know how I can drink a beer that would best complement a fish such as tilapia or hake.

When it comes to wine, it's said that white pairs well with fish, and red with meat. Is there any similar rule with beer?
Take your cue from recipes for fish cooked in beer/ale.  "Ale" (not usually specified further) and "amber beer" (example) seem to be the most common, and I can say from personal experience that these work well both for poaching fish and drinking alongside baked, broiled, or grilled whitefish.1  Of course, how your fish is flavored may affect your beer choice, but that might be a question for Seasoned Advice.  If the dominant flavor isn't the fish but, say, curry or habenero, that's a different matter.

Anecdote: In the context of a renaissance-themed event I once cooked from a 15th-century recipe for whitefish poached in ale.  I consulted my local brewing experts and together we made the ale (recipe and documentation).  They told me that the key difference in that time period was that ale didn't use hops.  There were no leftovers.  Based on that experience, I usually reach for a low-hops medium-strength beer to go with whitefish.

1 I don't eat a lot of deep-fried fish so can't advise there, sorry.  @Hunse suggests in another answer a sturdier beer for deep-fried fish.