Ugh. I used to get ingrown toe nails on my big toes really badly. I used to just cut them out, but you have to be extremely sterile when you do so because it can get infected easily. I think, it's been a few years, that mine got infected even though I cleaned the scissor/clipper with rubbing alcohol before cutting. Anyway, it was tremendously painful - I couldn't run or anything, it was terrible. I went to the podiatrist and there is a simple procedure where he applies local anasthetic to the toe then cuts away the sides of the nail that are under your skin plus a little bit more. Your toe nail is a little bit narrower, but not much. Anyway, he then applies a chemical to the area that he cut out that kills the root of the nail where he cut out so it can't grow back. Basically, it gets rid of your ingrown toe nail problems forever. It's been 3-4 years and it has been great. Oh, and since it's just a nail, the recovery time for it is quite short - he told me that one kid was playing varsity football 24 hrs later. Personally, I needed a few days before I could do serious running, but I could and it didn't hurt.

However, I did have to do epsom salt soaks and keep my big toes really clean and put on antibiotics and bandaids for about 6-8 weeks, but it was well worth it - I just did it before school, after I played frisbee or whatever after school, and then before I went to sleep, so it didn't take up any time really, I was able to soak for 10-15 minutes while doing other stuff.
Anyway, that's another alternative if this is a chronic thing you're getting.
If this is just the first time, you might as well just soak your foot in warm water then get a really clean scissor/clipper (rubbing alcohol) and take care of business. I was able to get away with that for awhile, but it kept growing back.