Can I improve carb performance without buying a whole jet kit?
You can get about 90% of the performance of installing a jet kit by installing new main jets. Main jets are available from better motorcycle shops. You just bring in your old ones and tell them what size you want, or even tell them you want one size larger (richer) or one size smaller (leaner).
If you want to try finding jets on your own, the pilot jet is part number Keihin N424-25. Once you find that, you have to tell the jet size that you want. Stock on the F and J bikes is 38. The usual pilot jet for altitude compensation is a 35.
The main jet is Keihin 99101-393, and again you have to list the jet size after the part number. The stock mains you have should be 105.
The nice thing about jet kits is they come with instructions and are based on a lot of actual dyno research, so they get you in the ballpark right away. That's what you're really paying for. They also have much better needles than the stock ones. A Factory Pro kit is more expensive than DIY, but it's easier and faster.
What components are needed to rejet without a jet kit?
You don't need to spend 90 bucks on a jet kit.
Just put two or three washers under the needles for pods and another one or two for an exhaust pipe and you're 90% of the way there. It's that last 10% that can be difficult.
One thing to watch out for if you buy jets on your own: DynoJet brand jets have their own sizing system that doesn't correspond to Keihin jet sizes. However, we don't recommend DynoJet, anyway. Factory Pro is the recommended brand for the 250. DIY is cheaper, though.