Do you know how to value REITs? I assume the fact that you do not know how to buy them means you do not. That is great because it makes the answer fairly easy. In which case I would recommend the vanguard REIT index fund or etf (vgslx or vnq). You can buy this anywhere, but the best place is vanguard. In fact, you do not even have to use the vanguard fund if you have another index fund available to you with a low expense ratio and low trading fees.
You should note that the bulk of returns from REITs are in the form of ordinary income. To qualify as a REIT, the corporation must pay out 90% of its earnings to shareholders. I believe this allows the REIT to avoid taxes, so it is passing them to you. This makes them about the most tax inefficient investment vehicle. So, I would highly recommend you keep them in a tax advantaged space of some sort.
Start by going to vanguards site and reading about the reit etf: vnq.
I must ask, what is your plan here? Are you planning on setting REITs as a percent of your portfolio, say 5% and keeping it at that? I ask this because US REITs kind of look like a bad deal. The valuations are high right now due to everyone reaching for yield. If you simply want to have a 5-10% of you total portfolio allocation to REITs, they might be a good idea. However, if you have a different approach, I would be very cautious to advise you to buy REITs right now.