First found an theme you like from any site. Download that theme to on your computer first. The theme come in an zip file. Don't unzip the file at all. If you are running your forum with Tiny Portal make sure you get the right theme not the wrong theme. If you do get the wrong theme and try to install it's will cause problem's with Tiny Portal. If your forum is SMF 1.1 RC3 Version please make sure you get that theme version.
Log into your forum then go to your Admin Panel. Go down and you will see Configuration after you see that. You will found Themes and Layout hit that.
In Themes and Layout you will see this Themes are the different looks and feels of your forum. These settings affect the selection of themes, and which themes guests and other members use.
Here what it's look like

After you see that you will found under that Latest and Greatest Themes. Keep gonna down and you found Install a New Theme.
Here what it look's like

Hit browse on the new theme and found that theme on your computer and hit that zip file.
Here what it look's like after you found that theme

Hit install!
A window will pop up.
Here what it look's like

Hit ok and it's will install the theme.
If the theme installed successfully. It will say's
Installed Successfully
"your theme" was installed successfully.
That's is how you install an theme on your forum.