After you unpack, the contents should have README and/or INSTALL files which describe how you exactly continue from there on. There might be an installer script, like install.sh
(or .run or whatever), which you could use like
chmod +x install.sh
(the above makes it executable, no need to do that more than once)
or if the package has source code inside, like many do, then you really want to read the INSTALL etc. files, since every build procedure can differ from all the others. A common way is to
./configure && make && make install
which configures the sources, compiles them and installs (needs to be run as root, the last step, but if you do it in one line like the above, you'll have to be root when doing it; the && marks make it work only if it succeeds). If configure fails, you may need to install some other software that is needed, before you can continue; if/when it fails, it should drop you a line or two and tell what went wrong. Once it goes well, make should compile it; only after it succeeds should install run, copying the compiled files to your system.
Read the documentation that comes along. And the websites if any.