Distributions often ship with only one package manager to keep things simple. I don't know if it's wise to start adding another package manager to your system, and yum is perfectly good to add rpm packages to your system. If amule is in the yum reposities, you just hit a command
and see what happens. Though most modern distributions nowadays have graphical front-ends to their package managers, so if CentOS is a "modern distribution" you should perhaps crawl trough the menus to see if there is such a program. I personally prefer using console, but if you find it easier for yourself, see if there's a graphical front-end for yum somewhere.
If the above yum command says it can't find amule (the package name you ask to install should not contain any suffixes or version numbers, just the name part of the filename), you may have to add a new reposity to yum which holds the packages that are needed. This is easy, and there are basically two ways of achieving it:
1) you find out the information (i.e. address) of the reposity and create a new repo file under /etc/yum.d/ (that's the directory on some other RPM distributions, might differ on CentOS), taking one of the existing files as an example of the file format
2) you find an rpm package from the web that, when installed, adds the new reposity to yum. This is a lot easier if such an rpm is available; effectively it does the same as above, but without you needing to use editors yourself.
After that, update yum's knowledge of reposity contents:
and then re-try installing amule.