Note: Obviously, there are two distinct plots in The Two Towers. There is the story of Aragorn and Company teaming up with the Riders of Rohan to face off against the troops of Isengard (which takes up the first half of the book), and there is the continuing Ring quest (which occupies the second half). But since we started The Fellowship of the Ring with the Ring quest, that's the plot line we are going to pursue here.
Mordor or Bust
At the beginning of Book Four, Frodo and Sam finally catch Gollum spying on them. Frodo forces Gollum to swear an oath to lead Frodo into Mordor. From the get-go, things aren't too hot for our dynamic duo. Frodo and Sam need help getting into Mordor because they are completely lost in the rock fields of the Emyn Muil. But the guide they manage to find, Gollum, is only in it for the Precious. He swears on the Ring that he will help Frodo, but both the hobbits know that Gollum will stop at nothing to take back the Ring that has taken a hold on Gollum's mind.
The Sneak and the Hobbitses
Gollum leads Frodo and Sam towards Mordor, sure, but his motives appear unreliable, so Sam watches the little guy carefully for any sign of treachery. When he overhears Gollum arguing with himself in Book Four, Chapter Two, he discovers that Gollum is literally of two minds about helping Frodo with the Ring quest. On the one hand, Gollum's good side knows that he has promised on the Precious to help Frodo. Gollum's bad side doesn't care. He wants to lead Sam and Frodo up to a dark place where they will meet their deaths so that Gollum can steal the Precious back. Having overheard Gollum's arguments with himself, Sam knows to be suspicious, but we don't know yet whether Gollum's good side or bad side will win out.
When Frodo and Sam meet up with Faramir of Gondor, he seems like a huge help. Sure, at first they worry that Faramir is going to try to take the Ring, but (a) he doesn't, and (b) he gives them supplies to take with them into Ithilien. But if Faramir is friendly to Frodo and Sam (once he realizes that they didn't betray his brother Boromir), he is downright threatening to Gollum.
Faramir thinks Gollum looks evil (which is a bit prejudiced of him, we'd like to point out), and he almost gives his archers permission to shoot Gollum at the pool of Henneth Annûn. Frodo saves Gollum from this threat, but Gollum mistakenly believes that Frodo is conspiring against him with the men of Gondor. Convinced of Frodo's betrayal, Gollum's bad side starts to get the upper hand, leading to horrible, spidery consequences for Frodo and Sam.
… Shelob, that is. Despite the concerns about Gollum that Faramir expresses to Frodo, Frodo decides to keep following Gollum into Mordor. Gollum leads Frodo and Sam into a long, dark tunnel in the mountains bordering Mordor, to a place called Cirith Ungol. where the climax of the novel takes place. This mountain pass is the home of Shelob, a giant spider. And she really likes the taste of young hobbitses.
While Frodo is busy trying to fight Shelob, Gollum suddenly jumps on Sam out of the dark and tries to strangle him. This showdown finally answers once and for all if Gollum's going to be a good guy or a bad guy in this story. He may have promised Frodo to help, but in the end, Gollum is out for the Ring, and he'll murder our heroes to get it. Now, we just have to find out how Frodo and Sam are going to get away from Cirith Ungol to continue on with their quest.
A New Ring-bearer
After beating up Gollum in Cirith Ungol, Sam runs to confront Shelob. By holding up Galadriel's jewel and stabbing at Shelob's many (disgusting) eyes, Sam manages to scare Shelob away from Frodo. But Shelob has already bitten Frodo, leaving him dead(-ish). A despairing Sam decides to take up the Ring and go on to finish his master's quest before allowing himself to die.
Wait. What Happened to the Old Ring-bearer?
Uh oh. After eavesdropping on some orcs, Sam finds out that Frodo is still alive. Yikes. Apparently all Shelob has done is paralyze Frodo, so she can save the good eatin' for later. Now Sam resolves to rescue Frodo, because he didn't really want to bear the Ring all that much in the first place, thank you very much.
Samwise Gamgee to the Rescue
The conclusion of The Two Towers is not much of a conclusion at all, to be frank. It merely sets the stage for the final installment of the Lord of the Rings series. On the minus side, Gollum isn't going to help our guys destroy the Ring. On the plus side, Frodo and Sam are both in Mordor, which is where they've been trying to go this whole time. Now, if only Sam can rescue poor Frodo from the orcs, they will be in good shape to continue the Ring quest. That's where The Two Towers leaves off, so you'll have to check out The Return of the King to finish off the story of the Ring.