- <img src="http://www.yourwebsite.com/somepicture.jpg">
At this time, LiveJournal cannot host images other than your userpics. Your image must be hosted on a webserver that allows the pictures you store there to be referenced by other sites (this process is also called remote loading).
Normally, your Internet Service Provider (ISP) will offer you some free web space as part of your monthly account. You should check with them and find out if they allow remote loading. If your ISP doesn't offer web space, or doesn't allow remote loading, there are numerous freehosts with differing policies.
One good thing to try would be if you see a picture that you admire on someone's site, ask them! If you can't get their email address, just leave a comment in their journal; most LiveJournalers are happy to assist each other.
Thanks fionacat :o)