In the launcher options, increase the maximum memory option. The maximum memory is specified in megabytes, so if you want to set 4 gigabytes of ram, you would use a value around 4,000.
The minimum RAM is less important but increasing it tells Java to ask for that amount of memory right away, rather than continually asking your computer for more RAM when Java needs it (up to the maximum).
Make sure that you have 64-bit Java if you want to use more than approximately 2.5 GB of RAM. Mac OS X users already have 64-bit Java, but Windows and Linux users can download 64-bit Java from Oracle's website (Linux users can also install OpenJDK).