You read the package's .dep file, which lists dependencies, add those to your install queue in the right order and then install the queue.
It's not as daunting as it sounds, since the default Slackware installation already includes most common dependencies.
The most dependencies I ever had to install for a package were 3. But if you need a lot of additional software with many dependencies, it's best to do it just once for installing slpkg and then let that tool deal with it.