Traditionally, we ignorant youths are taught that, when a bank receives a deposit, it only needs to keep a fractional (let's say 10%) and can lend the rest of the deposit out.
Then, I've seen it suggested that banks can keep the deposit as the full excess reserve and create money on top of that, such that the deposit is 10% of the total.
ie. someone deposits $10; the bank then creates an additional $90 (for lending) to total $100, and keep the $10 as the 10% reserve
More recently, I've seen people say that banks can actually just create their own money altogether, which they can then lend out. I don't understand this because, if this is the case, why do central banks need to engage in open market operations to increase the money supply???
Please help. I am clueless!
If you haven't seen it yet, The Ultimate Beginner meta-thread offers quite a bit of links to resources on a wide range of topics.
For this one in particular, if you want to get to details, here's a good section of resources:
Federal Reserve
In particular, "Modern Money Mechanics" is probably the most authoritative source, but if you need something a little more understandable, The Creature from Jekyll Island & The Mystery of Banking ...are really the best place to start. (you can find links, including one to a free PDF download there).
The reason you've seen it explained both ways is because both things actually happen.
See here. This film series offers a pretty well laid out explanation of how the system works, but of course, has flaws of its own. It's still definitely worth a watch, as it'll help to begin to wrap your head around the concepts of the banking system. That link will begin at a relevant point for this particular question. You'll see how money is created out of thin air, as well as how money deposited gets loaned out.
The playlist including those films is here.
Here's a decent video on that shows the accounting of the deposit part of the system: