I'm not sure if this is the best way, but it's worked for me. I've stripped all the line off the reel, wrapped it all really tightly around a smooth garbage can, taped it so it would move and let it sit for a few days. Did the trick for me.

I like to wrap my line around an old tin coffe can. Wrap it tight, but not tight enough to really stretch it. Leave it on overnight and then put it back on the reel. This should work for you.

I actually like to do the same thing as the answers above, but on a nice day when you don't have a lot of time I will just unreel the spool and lay the line out in your yard. Let the sun warm it up a little, but don't forget about it. Then as long as I have it off the reel, check it for cuts etc... Then when I reel it back on I pull the line through a cleaning solution for fly line, if you don't have that use armorall. It helps the line shoot through the eyes too.

If it is kinked to the point that you can feel a crease in the line, then get new line. Be careful about stretching your line tight like a guitar string because when you do this it opens up microscopic pores in the line and it can hold dirt and become brittle in sunlight. If it is not creased then simply put it around a plastic coffee can and set it over a heat vent in your floor for a couple days. This will help relax the line, then rewind onto reel.

If I were you I would just replace it.

Take it off the real and soak it in hot water for a while then put it back on the reel.