Step 01:
Go download and install Quantum GIS - now you have a GIS program to begin using!
Step 02:
Get some background data to overlay your mapping info on, I'd suggest starting at the Seamless USGS Site
Click on the area labled View & Download United States Data; depending on your computer and internet connection, the new page might take a bit of time to load.
This is the new page that loads, now you'll need to zoom to the part of Alachua County where you'll map. As with many internet sites, allowing your mouse to hover over a button on the left side will typically bring up a small info label telling you what the tool is for. Use the zoom-in tool to zoom in on Florida.
Watch this video to see how you can use the site to zoom in and download background imagery for all of Alachua County (although I'm only doing it for one small part).
Once you've saved the file, you will need to go to the directory you chose to download it and unzip the file. This should be relatively straight forward. All you will need to do typically is double-click on the file and then copy the contents into a permanent directory. Again, this can be of your own choosing.
Step 03:
Now that I have a background image that I can use as the backdrop for my counter-mapping project, I need to open that image in the Quantum GIS program. Start the QGIS program (which you should have installed as step 01 outlined above).
So, there you have it, the nuts-and-bolts of working with GIS data. Obviously, it can get as complicated as you want, but hopefully you see the potential in being able to so quickly begin making maps.
The main idea here is to (at first) play around and enjoy computer mapping. I know that this is a short introduction and it may not seem like I covered every single base; maybe that's true and maybe it's not. Regardless, the main point is don't be afraid of your computer. After all, if you screw things up, you can always delete it and start over!
Most importantly, have fun! You have already started making maps. If you want more direction, see the links section for webpages, books, and articles.
to zoom in on Florida.