There are several ways you can do this, but the most common is to put on a Web Server, do a little research on your part and decide where to store your pictures/information.
If you have DSL or Cable you are can always be connected to the Web, you can skip finding a Web Server because that is what your going to make your home computer. If you have a regular modem connection proceed with the info below.
You may have "Free" Web space available through your local ISP, or you can simply signup at one of the many "free Web Hosting" sites available. I prefer to do the second route as you never now when you maybe switching ISP's (many competetive plans available).
Once you have decided on a Web Host, you can signup and use the provided tools and instructions that are usually available. Geocities is one place, and Homestead as well, I believe you can locate dozens if you try, pick one that has good instructions and tools for you to use.
to start your search.
Just follow the instructions on creating a "web page" once you pick a site, you can make the page you create fancy or just pain boring (my case). Homestead has a tool that makes uploading your pictures easy and then you can paste them on the page anywhere you like.
I suggest you upload pictures from work if (on your own time of course) they are Internet enabled. You are looking for a fast transfer time if you are impatient like me, otherwise a modem is fine.
Thats basically if;
1) Transfer images into a computer (scanner / direct from digital camera / cd - availabel while processing regular film). You can do this at home or work.
2) Upload to Web Server or File Server that you have created space on with your own page.
Figure about a hour to set up your site, once you do you will be glad since you can store family pictures or anything you want on other pages you create. Most importantly all this is available from any computer connected to the Web.
Let us know if you hit any snags along the way.