This post is now edited completely to work with the new forum changes. Mostly the way to upload is the same, just where to go and how to get there is a bit different. To minimize confusion, I have images to help.
There are several ways to get to the place you need to get to. The first is the navigation in the top right corner.
The main navigation on the left side above the message boards.
Select FORUM ACTIONS and then either EDIT PROFILE or GENERAL SETTINGS
Once you have selected any of the above options you need to look on the left side of the screen and find the MY SETTINGS option menu as seen below:
Select EDIT SIGNATURE to add or change a signature (siggy). If you have one already it will show a preview of your current signature and below that you will have this display (which is modified with text to ensure you go to the right spot.)
You need to go to photobucket.com and sign up for a free account unless you have one already. Upload the image you want to add as a signature to photobucket. Please do not use any pre-exisiting photobucket uploaded link from someone who has made one for you as it will be linked to their bandwidth. You will want to use your own. Copy the URL with the IMG coding in it and paste in the text area of the signature space. DO NOT, I repeate, DO NOT upload your signature from the computer in the upload section because it WILL NOT save as the correct size or quality.
For Avatars chose EDIT AVATAR and you will get this screen.
Any of the options here will work, but in my opinion uploading avatars from the computer directly has the best quality in this option. Some of mine have been blurrier when added from a link. Make sure to pay attention to the sizing listed beside the upload options. If it is over 100x100 it will either resize or not upload. If it is over 19.5 KB it is likely not to upload directly. You can use a photobucket link to do one over that size, but sometimes it will not work if the file is too much larger than that.