Login or signup if you have yet to do so, then go to the Upload page,
http://en.wikipedia.org/wiki/special:upl...
check that the picture you want to upload is allowed (i.e. you took it yourself or it meets the conditions described on that page).
Then browse to the file on your computer in the 'source filename' box, edit the destination filename (which is the name you use to insert the image on other wiki pages, below - eg MyPhoto123.jpg) and enter information about the source and copyright holder in the summary box. When you've done that press the upload button.
Then go to the page you're wanting to put the image on, edit it and use the code,
[[Image:Image name|thumb|Caption]]
if you want the thumbnail to appear (as a link to the full image), or
[[Image:Image name|Caption]]
to insert the original size image into the article. (Caption is the description that appears when you hover the mouse over the image, and which appears under the thumbnail)
eg
[[Image:MyPhoto123.jpg|thumb|A moose]]
[[Image:MyPhoto123.jpg|My photo of a moose]]
You can experiment with the code without making changes to an actual article in the wikipedia sandbox:
http://en.wikipedia.org/wiki/wikipedia:s...
For more information see the page about uploading images on wikipedia:
http://en.wikipedia.org/wiki/wikipedia:u...
Lastly, you can see a list of all the images already uploaded:
http://en.wikipedia.org/wiki/special:ima...