Well, it is Russia, so even going to the post office is Orwellian. Registration is done by one of two methods, and it doesn't really matter who you receive the invitation from. If you're staying in a hotel, let them worry about it. If you're staying in an apartment, the landlord is responsible. If you're staying privately (with a friend or something), you need to go to the nearest post office and register there. Your friend will need to go with you and take their passport as well. They have you fill out this long form, take photocopies of your passport and the passport of the person you're staying with, and then mail in your registration. They tear off the bottom of the form to give to you as evidence that you've registered. It's a hassle to deal with the post office hags, but it's better than the old days of OVIR.

In reality, my experience recently has been that they're not even really looking at registrations that much anymore. It's still required, of course, but the last two times I've left the country, they glanced at my passport, stamped it, and out I went. They just waved their hand and smirked when I tried to show them my receipt for registering at the post office. I talked to another guy who said he hasn't been asked for evidence of registration in the last 9 trips over 2 years. This whole dust-up with Georgia could change that, however, so I'm still making sure I do it.