It doesn't matter what image editor you use, it simply must be saved as a jpeg or gif. Anything else will give you problems, especially bmp's. I've seen .png used before, but rarely. I'm not sure what stipulations they have.
That's the easy part. The hard part and most difficult to explain is hosting your pictures. Last I checked, this forum doens't do that for you. You'll have to sign up sompelace that will lend you server space. Freeservers.com is a good start and even tell you how to use FTP. (Don't let the terms intimidate you, it's not as hard as it sounds!) When you get there, you'll understand what FTP will do for you. Basically, it takes your file and copies it onto a server so that it can be accessed on the internet. I might also recommend using filezilla's FTP client. Free, easy to use, no BS. I do plan to write a web page specifically for forums because I found this to be one of the most asked questions.
A few other tips:
Stay away from Geocities! Not enought traffic to support pictures worth a crap.
There are some servers that are built specifically for this purpose! I can't give you any names right off, but if you went to a search engine and typed in "free picture hosting"
If you need more help, drop me an email.