It is a great book series, and you will not be totally lost. Just keep in mind that things have changed since the series finales, and you'll be fine.
Where can I find out about the changes before hand? I tried the wiki and it didn't really help much...
A rough guide to what you need to know before
Destiny, post-DS9 and post-NEM:
- Riker is CO of the
USS Titan, which is far, far away from the Federation on a mission of exploration, along with his wife Troi and Commander Christine Vale, who served as
Enterprise-E security chief. Riker and Troi are trying to conceive a child
- Picard is still CO of the
Enterprise, and Worf has chosen to leave the Diplomatic Corps and come back to Starfleet to serve as the XO. Picard and Beverly are married, and Beverly is pregnant.
- Picard and Co. fought off two attacks from a single Borg cube in 2380, a year after NEM. The cube had been stranded in the Alpha Quadrant when
Voyager destroyed the Borg Collective's transwarp capabilities in their series finale. This attack led to the death of Kathryn Janeway.
- Just before NEM, the Federation held a special election after Federation President Min Zife of Bolarus resigned unexpectedly. Nanietta "Nan" Bacco of Cestus won the election.
Destiny takes place during her second year in office.
- Shortly after the DS9 series finale, Ezri Dax chose to transfer to the command track. She eventually worked her way up to the rank of Lt. Commander and transferred off of DS9.
- The Romulan Star Empire has split into two: The Imperial Romulan State, led by Donatra as Empress, and the Star Empire, led by Tal'Aura as Praetor.