In general only the root user can give a process a higher( lower number) priority. Users can only give a process a lower( higher number) priority.
NORMAL USERS ONLY
In general for normal users, they can use the nice command but probably wouldn't because they have the best priority they can get with the default priority they are assigned, usually around +10 or so. They can, however, use nice to give a process a lower ( higher number) priority, if it is something that can take its time to complete.
ROOT USER ONLY
For the nice command you can do something like this. It will give it the lowest priority possible. However, this can be dangerous if the process is CPU intensive. It could severly slow down your box! I would never go below -10, if your system priority goes from +20 to -20. Some OSs are different.
nice --20 /path/to/some/process
to change the nice value of this process.
renice -10 /path/to/some/process
Notice that I used 2 -- in the first example. The first dash is for the option. The second one is for the "sign" of the priority. You must give it a negative sign in order to increase the priority. REMEMBER, ONLY THE ROOT USER CAN INCREASE PRIORITY OF A PROCESS.
Read the man pages for more detail on this topic. man nice and man renice.
