Solitaire is a simple marble game, the rules and further information can be found here:

To play the game you simply need to download the zip file and extract the contents straight into your mIRC directory.
Once you've done that, open up mIRC and type "/load -rs solitaire.mrc" into one of the windows.
Then you should be able to play by right clicking in the channel and going to games - solitaire (or similarly through the commands menu at the top).

Once the game is open it's all fairly self explanatory, and if you're confused by anything then clicking the big help button should clear any problems up.