My Mac is running slowly and having some glitches in opening programs. How can I clean upspace?

Try Disk Inventory X

http://www.derlien.com

and ONYX

http://www.titanium.free.fr

learn how to use Recovery Mode

Don't do anything until you can restore and have repaired the disk drive.

Post should get moved to either ML (10.8,.4) or iMac forum

Swap out the hdd for an SSD : )

Don't do anything to clean it up unless you don't know how to first remove browser history from within the programs; low on disk space (I consider more than even the 15% minimum, more like 3--40%)

And do you have page outs? more than enough RAM? what actually leads you to ask? Programs aren't opening properly?

Sometimes it is easier to take the long road: just reinstall and restore.

Recovery Mode

http://support.apple.com/kb/HT4718

TimeMachine 101

https://support.apple.com/kb/HT1427

http://www.apple.com/support/timemachine

Mac OS X & Mountain Lion Community

https://discussions.apple.com/community/mac_os

General purpose Mac troubleshooting guide:

Mac OS X: Starting up in Safe Mode - http://docs.info.apple.com/article.html?artnum=107393

What is Safe Boot, Safe Mode? (Mac OS X) - http://support.apple.com/kb/HT1564

Isolating issues in Mac OS X

Creating a temporary user to isolate user-specific problems:

Isolating an issue by using another user account

Identifying resource hogs and other tips:

Using Activity Monitor to read System Memory and determine how much RAM is being used

Starting the computer in "safe mode":

Mac OS X: What is Safe Boot, Safe Mode?

To identify potential hardware problems:

Apple Hardware Test

General Mac maintenance:

gliches when opening programs

What sort of glitches?