Some of the features that MobileMe users have come to expect are going to be cut down the road, but for the time being they will still be able to access Gallery, iDisk, & iWeb publishing. As of June 30, 2012, the features will no longer exist; be prepared, the day is coming.
Make a back up of your contacts, calendars, and bookmarks. If something goes wonky during the transfer process, you will need this backup to restore any issues. You can back up each one by opening the respective app and going to File >Export. Save the file somewhere safe!
You will see a progress bar showing you exactly how the process is going. After it is all said and done you will see a screen similar to this, letting you know that you need to continue the setup process on your devices.
That's all there is to transferring your MobileMe account to iCloud. It's a bit intimidating at first but as long as you take your time, ensure everything is up to date and you have a good backup of your data, you shouldn't have anything to worry about.