TPM does not provide their bloggers with disk space for graphics files. They must be remote-loaded from a different server. Additionally, media files can only be placed in the original blog posts. Comments to blogs have a very small, limited set of html tags enabled.

There are many free image hosting services available on the web. You need to decide which of them are best for your needs. If you desire to keep complete copyrights to your created images, carefully read the services' TOS. If you are one who prefers to stay somewhat anonymous on the net, read the privacy statements; often they pretty much state they will use any and all personally identifiable information you offer up, anyway they are able to derive income from it. It's a good reason to create an extra free web email account.

Once you have chosen a free image hosting service, most will give you the html code for posting any uploaded graphics files, so that part should be easy.

One other consideration you should make is that TPM is laid-out with a fixed width, and the maximim width for agraphics file in a user's blog is around 430px.