The best way--pretty much the only way for most foreclosures--is through a Realtor. In most cases (there are a few exceptions with lenders who sell direct), a foreclosure is put back on the market through a Realtor. The property is listed on the MLS.
So, for most properties, your agent would search (probably with an automated search) for properties meeting your criteria, just as they would do for non-foreclosures. However, in many/most MLS systems (such as the one I have access to), I can specifically limit my searches to (or exclude from my searches) foreclosures.
Any properties listed on the MLS should be picked up by all the regular feeds--Realtor.com, Trulia, etc. So, pretty much you can search them yourself. The problem is that sometimes they go under contract very quickly. Meanwhile, it might take a few days for the information on your local MLS to make it to all the other sites. So I'd suggest both approaches: You look yourself on MLS-accessible sites. Many agents in your area, I'm sure, have that function on their sites. And those will be real-time. But I'd also suggest you work with an agent who can input your parameters (price, location, size, etc.) so that you'll be immediately notified any time a new property meeting those criteria come on the market.
The bank, in most cases, deals with the listing agent--the agent it's chosen to list the property. However, there will be multiple agents and it'd be better for you anyway to deal with another agent--a buyer's agent. So don't worry about which agent might be listing the property.
Hope that helps.