Like Peeta, Finnick first appears in this book as a shadow of his former self. He's mentally deranged and tortured by the idea that the Capitol might be hurting his captured lover, Annie. It's not until Katniss tells him about a special weapon that Beetee has created for him that Finnick starts to come back to himself, and "actually sounds like the guy [Katniss] met at the Quarter Quell" (6.51). It's a tough process, but he's a strong guy.
Finnick is one of the few survivors of two Hunger Games. Of those survivors, he's a lot like Katniss, a strong warrior and someone who is good at strategizing. He might have been forced to kill or be killed in the arena, just like all the other tributes, but he's also one of the few truly good people we come across here.
Eventually, Finnick finds the strength to carry on as he's waiting for the rebels to rescue Annie and is able to help Katniss through the parallel pain she experiences while waiting for Peeta. At one point, in a moment of astounding bravery, to provide a distraction for a rebel rescue operation, Finnick publicly (on TV) reveals exactly how Snow abused him. As Katniss's reaction shows, she and just about everybody else had misjudged Finnick:
That explains it, then. Finnick's parade of lovers in the Capitol. They were never real lovers. […] I want to interrupt the taping and beg Finnick's forgiveness for every false thought I've ever had about him. But we have a job to do and I sense Finnick's role will be far more effective than mine. (12.28)
Finnick had no choice but to be Snow's prostitute, but he used his time as one wisely. While everyone else thought he was a rake and a playboy, he was collecting dirty little secrets about the higher ups in the Capitol, waiting to reveal them until the right time. The right time happens to be this TV airing, and he manages to indict nearly every power player in the Capitol. Now that takes guts.
Katniss might not be able to decide whom she loves for much of Mockingjay, but Finnick never has that problem. It's always been Annie, and once he's reunited with her, he really starts to act like his true self:
It's something to see Finnick's transformation since his marriage. His earlier incarnations – the decadent Capitol heartthrob I met before the Quell, the enigmatic ally in the arena, the broken young man who tried to help me hold it together – these have been replaced by someone who radiates life. Finnick's real charms of self-effacing humor and an easygoing nature are on display for the first time. (17.52)
At least he has a little true happiness. One of the most heartbreaking events in the book is when Finnick dies while Squad 451 is moving through the tunnels underneath the Capitol. Katniss watches his death in disbelief:
Far below, I can just make out Finnick, struggling to hang on as three mutts tear at him. As one yanks back his head to take the death bite, something bizarre happens. It's as if I'm Finnick, watching images of my life flash by. The mast of a boat, a silver parachute, Mags laughing, a pink sky, Beetee's trident, Annie in her wedding dress, waves breaking over rocks. Then it's over. (22.52)
It's as if after making it through two Games, Finnick's forced back into the arena to die, killed by the same kind of "mutts" that he and Katniss fought in the arena. He leaves his new happiness behind to protect Katniss and the new world they're fighting for, and to protect, although he might not know it, his unborn child.