The best way to install Wine would be to install the Slackbuild.
The Slackbuild HOWTO will tell you how.
Here are some learning tools you will find useful:
. It's a little bit dated but still quite useful on the basics of how Slackware operates.
The Slackware Documentation Project
. (Edit: I see Kustom42 has already pointed you in that direction.)
. Machtelt Garrels's Intro to Linux. PV does not believe in changing stuff just for the sake of changing stuff, so basic Linux methods generally still work. I found it an invaluable reference when I started; I still have a printed-out copy on my bookshelf.
The Slackware forum right here at LQ is the "unofficial" official Slackware forum--it's a great place for help.
I started with Slack and I'm glad I did. Once you understand Slackware, no other distro will ever intimidate you, because Slackware will teach you how to figure stuff out, while also giving you a fully functioning distro to use for general computing while you do.