There are three basic ways to install software in Slackware: install a pre-build binary package, make your own package, or compile the sources and install the resulting binaries manually. If you need to compile a program from source code, making it into your own package is easy and useful. Here's how these methods work.
To install a package you first need to get the package.
.tgz or .txz and looks something like “mozilla-firefox-14.0-x86_64-1.txz”. The more universal naming scheme is “PRGNAM-VERSION-ARCH-BUILD.txz” where ARCH denotes the architecture for which the package was built (examples are x86_64, i486. armv6l, armv7hl, noarch) and the BUILD number is not just used to mark incremental package updates but also allows community packagers to add their own build tag1) which makes them unique.
To install the package you need to change to the root user. Run either the command su - or sudo -i and enter your root password. Now run the command
upgradepkg --install-new your-long-package-file-name
You should see a bunch of text running across your screen telling you about the package being installed, and possibly about an old package it might be replacing.
The recommended way to build packages from source is to use or create SlackBuild scripts.
However, there are other utilities such as slacktrack (part of Slackware itself), src2pkg and checkinstall which automate the package creation process entirely (with a few user inputs), but these are not guaranteed to work with all possible kinds of source projects.
Binary packages from other distributions can be converted to Slackware packages by using conversion tools. Although building packages from source is always better, there are some situations which might warrant the use of these tools.
Some users still prefer the traditional method of compiling from source directly and installing using make install or a similar command.
The generic steps for standard GNU Autotools Makefiles are:
./configure make make install # as root
The configure script may take additional switches to enable or disable features or configure other build options.
Other build systems may involve different steps, depending on how the source project is set up. As always, it is best to read the upstream developer documentation to figure out how to compile and build a program for your system, including which dependencies to fulfill.