Checking the space
You can use OmniDiskSweeper to check what is occupied your space. It's free.
Or, if you like command-line, run Terminal.app and enter this:
du -kx /some/directory | sort -nr > $HOME/DiskUsage.txt
you will get sorted size-list (in kB) for all directories under the /some/directory.
Another check - swap file. If your apps take more memory as you have, the OS do "swap" parts of memory into HDD. (In the linux or FreeBSD there are usually dedicated HDD partitions (slices) but on OS X these are files.
You can check their size with:
ls -l /private/var/vm
you will get something like the next:
-rw------T 1 root wheel 4294967296 23 jún 14:30 sleepimage
-rw------- 1 root wheel 67108864 15 jún 09:03 swapfile0
-rw------- 1 root wheel 67108864 23 jún 14:54 swapfile1
-rw------- 1 root wheel 134217728 23 jún 14:54 swapfile2
-rw------- 1 root wheel 268435456 23 jún 14:54 swapfile3
-rw------- 1 root wheel 536870912 23 jún 14:54 swapfile4
-rw------- 1 root wheel 1073741824 23 jún 14:54 swapfile5
As you can see, in my HDD are now 5 swapfiles with total size 2GB. When start too much programs (or have 50 browser windows or soo) sometimes the swap increases up 5 GB or more. Simply close applications and the swap will be freed.
The another 4GB file (sleepimage) is the space, where OS X store its memory content when going to sleep (SafeSleep - storing memory content in the file). While it is possible turn of the SafeSleep and get 4GB HDD space (or less, if you have less memory) via pmset command, i do not recommend this.
When you browsing a lot, Safari storing some content into his cache/files. You can partially clear from the menu: Safari -> Empty Cache
Or simply check your cache files in the
$HOME/Library/Caches with the OmniDiskSweeper or the
du -kx $HOME/Library/Caches | sort -nr command from the Terminal.
You can Trash everything from the $HOME/Library/Caches without problems, but (for the safe) is better relog or reboot after the delete.
Another space-waste can be the Logfiles. You can check them with your Console.app (Utilities). (in the bottom left corner it showing the current size) - You can trash a big ones from the application directly.