For DS9, just read these:
http://memory-beta.wikia.com/wiki/DS9_relaunch
Avatar, books 1 and 2, are kind of a "season 8" pilot for Deep Space Nine, and the books continue from there. The link also lists several related books and comics. The comics aren't important.
Some of these books are kind of hard to come by, though. (In the chart, you can see some of them are reprinted... but not all.)
My advice - A Stitch In Time (a standalone book about Garak's past) is incredible, but expensive used, so skip that unless you have an overabundance of money or an ebook reader. Start with the reprint Twist Of Faith, which begins with Avatar and takes you through the next few stories.
I guarantee you'll be hooked. These books are *awesome*.
If you feel like adventuring elsewhere, my personal recommendation would be the Destiny trilogy (just search amazon for Star Trek Destiny), which is a big crossover thing that takes place 2 years after Nemesis, and will give you a good taste of all the ongoing stories that've started to weave together in the 24th century books. (The whole DS9 relaunch, in the link above, takes place before Nemesis, and Destiny only reveals tiny, tiny amounts of the DS9 relaunch story. It was designed so there's no need to read one before the other.) The story of Destiny begins with a full-scale Borg invasion, orders of magnitude beyond anything that was shown on the series, and that's not even the most interesting story in the trilogy. It's complicated, surprising, and really fantastic.
And finally, Vanguard is an original series set aboard a space station in the TOS era that is FREAKING AWESOME. The five books in the series so far are listed here:
http://memory-beta.wikia.com/wiki/Star_Trek:_Vanguard
Vanguard is, for my money, the best Trek Literature being written, and even if TOS isn't your thing you might want to check it out.
So there you go - DS9 relaunch, Destiny, Vanguard. Three really solid starting points; take your pick.
The advantage to DS9 is that there is a lot of it and it all goes in one order, so it's not hard to follow, and if you liked the DS9 show you're guaranteed to like the relaunch. On the other hand, some of it is hard to find cheap. (You can buy them all easily from amazon used, but some of them run $10-$20 for a mass market paperback.)
The advantage to Destiny is it opens up all of the ongoing post-Nemesis continuity, which is pretty sweet. Destiny brings together a lot of series (with no prior knowledge necessary), then afterwards they all spring off again - TNG, Voyager, Riker's ship Titan, and some other ships/people that show up every so often. And DS9 will jump forward to join it with a book late next year. And it's *all* worth reading; you'll be amazed. If you do go this route, and you like Destiny, anyone here will help you untangle all of the ongoing continuity, so don't worry about that until after you read the trilogy. It can all be a little overwhelming though, so that's the disadvantage here.
The advantage to Vanguard is that it is only 5 books and exists completely by itself. And it's awesome. And still in print. And I don't really see a disadvantage, unless you're allergic to the TOS era
(Edited to be more comprehensive. I know it's hard to figure out where to start, so I decided to be detailed.)