Re: I need help editing a jpg!
As a graphic designer I often get asked to include a logo in printed material and all they have is a low-res jpeg, so I've done this same thing many times. This is not retouch related so I'm not sure why you posted in this forum. Looking at your example, it can be easily done. You are not going to get any good result by tracing fonts--you need to replace them with actual fonts. You may not get the fonts to match exactly but you can get close enough that nobody will know the difference. This is a job for Illustrator! If you are not good at working in Illustrator, your best bet is to hand it to someone who can do it for you, unless you have the time and inclination to learn. The most time consuming part of all of this will be matching the fonts, unless you already know what they are. I believe I recognize 3 fonts. Really, you will save yourself A LOT of time if you can trace down the original EPS or AI file. Can you make some phone calls to find out where this came from and who might have the other version?
Anyhow, to answer your question, to do in Illustrator this first create a new file. Then choose file>place to put the jpeg in place to trace over. You'll have to trace out the shapes with the pen tool. Symmetrical shapes--trace one half and flip to make sure it is identical. As for the fonts, you have to find the right font and then type it in there. As long as the kerning is alright you can just go ahead and type the font in there in the correct weight and then convert it to outlines. From there you can transform the fonts into the right shape (ie. slanting backwards, extremely flattened, etc) Good luck.