So, Nemesis established that Riker would go off and captain the Titan, and once that status quo was established the books followed it. That created two ongoing series, a TNG series without Riker, Troi, or Data (with various new characters replacing them) and also a Titan series, with an all new crew.
There was also a very brief series, 4 novels and originally intended to be longer, about the Voyager crew after they returned home. That petered out, chronologically speaking, about 2 years in-universe before Nemesis.
At the end of last year, the Destiny Trilogy, a totally epic piece of whupass awesomesauce, tied those three series together as well as a minor thread from Enterprise (not necessary to have seen Enterprise at all, though, trust me) and made the greatest thing to happen to TrekLit in a really, really long time.
So the short answer to your question is: read Destiny. If you're just looking for a few books, jumping right in to Destiny is entirely possible, it'll bring you up to speed on anything you missed.
If you'd like the more comprehensive answer, here's everything else you might want to have under your belt to get all the continuity references in Destiny (again, I stress this is not at all necessary, but most of these books are also pretty great, so if you want to really immerse yourself, here's the plan, in a suggested order of reading):
Star Trek: A Time To Kill
Star Trek: A Time To Heal
Star Trek: A Time For War, A Time For Peace
These are the last three books in a 9-book series, but trust me, skip the first 6. They're fine, but they're not important. This series was written to lead up to the changes we see happening in Nemesis, and also establishes some pretty great stuff about the Federation government.
TNG: Death In Winter
This takes place right after Nemesis, and sort of fills a bunch of little continuity gaps right after that movie. Best read here, in the sequence, not with the rest of the TNG post-Nemesis books, which start up after jumping a few more months ahead.
Titan: Taking Wing
Titan: The Red King
Articles Of The Federation
Titan: Orion's Hounds
Titan: Sword Of Damocles
This is a suggested reading order, but you can move AotF later if you want; that's just where it was written. AotF is an interesting book, a year in the life of the Federation president. Pretty great stuff. The other four are, clearly, the first four books in the adventures of the Titan crew.
TNG: Resistance
TNG: Q & A
TNG: Before Dishonor
TNG: Greater Than The Sum
These are the adventures of Picard's crew post-Nemesis, and the last book leads right into Destiny. (In fact, if you want one book to read pre-Destiny to help fill you in on the changes, that's a good one; lots of fallout from earlier events, so lots of summarizing to get you up to speed.) This is probably the only set of books on this list that's variable in quality; a lot of people really dislike Resistance and Before Dishonor. Your mileage may vary.
Destiny: Gods Of Night
Destiny: Mere Mortals
Destiny: Lost Souls
AWESOME.
Then, the follow-ups:
A Singular Destiny
Titan: Over A Torrent Sea
Voyager: Full Circle
TNG: Losing The Peace (just coming out now)
Full Circle takes all the lingering narrative strands from the previous, abandoned Voyager books and ties them off, then takes the crew of Voyager through the next 3 years, through the Destiny trilogy, and beyond. And it is fantastic. Don't read the earlier Voyager books, just read Full Circle. A Singular Destiny is another unconventional look at the Trek universe, following an original character as we examine the fallout of the Destiny trilogy. TNG and Titan books are more traditional.
There are also many other brilliant ongoing series in Treklit right now, in particular Vanguard (an original crew aboard a space station in the TOS era), the DS9 Relaunch (following after the finale of that show, in-universe still about 4 years before the events of Destiny), and New Frontier (a wackier, wilder look at Trek that's just published its 17th novel). But if you're looking for the major, TNG-based continuity, that's what there is.
. Absolutely brilliant, and absolutely on the nose when it comes to Mack's opus 
