Backup your important data before upgrading.
Make sure your Mac meets Mountain Lion's requirements before purchasing.
See Step 1 > Apple - Upgrade your Mac to OS X Mountain Lion.
Your internet connection speed will depend on how long it takes to download Mountain Lion. See this tip on determining your speed.
Downloads speeds anywhere from 5Mbps upwards are ideal. Dialup connections could time out, and anything between dialup and 5Mbps could try your patience.
Apple strogly recommends using a high speed (broadband) internet connection as noted here > iTUNES STORE - MAC APP STORE - TERMS AND CONDITIONS
If you are upgrading from Snow Leopard directly to Mountain Lion, keep in mind, if you need to repair the startup disk or reinstall the OS X, assuming the instructions are the same as Lion, this requires broadband access (high speed internet) via Wi-Fi or an Ethernet connection.
If you have problems downloading apps, if you have anti virus software installed, disable that then try again.
Help for Error 100 ...
If that doesn't help, open the Finder. From the Finder menu bar click Go > Go to Folder
Type this exactly as you see it here:
Move the Cache.db file from the com.apple.appstore folder to the Trash.
Move these files from the Preferences folder to the Trash.
Move the com.apple.appstore.plist file from the Cookies folder to the Trash.
Empty the Trash, try the App Store.
If you see a dialog telling you the, "product distribution file could not be verified", reinstalling the App Store can help.
Download the appropriate combo update ...
If you are running v10.6, install the Mac OS X 10.6.8 Update Combo
If you are running v10.7, install the OS X Lion Update 10.7.5 (Client Combo)
Restart your Mac after the combo is installed.
Try the App Store.
Apps such as Little Snitch, anti virus software, MacKeeper can all cause problems when downloading apps from the App Store.