Equiping soldiers?

The Tutorial mode will teach you this right after it walks you through making the nanofiber vest. If you skipped it, here's the rundown:

Barracks-> View Soldiers-> Choose first soldier you want to change
Choose the "Loadout" button and you'll see 2 panels. The left one is your soldier's 4 equipment slots- Armor, Primary Weapon, Pistol, and "Backpack" (think of it as Accessory if it helps, dunno what good a backup vest does in your backkpack *grin*). The right panel is the available choices for whichever slot you click on your soldier's equipment panel.

Except for upgraded body armor, and most weapons, everything else for your soldiers will belong to the "Backpack" slot. Bad news- you can only choose ONE item at a time. If you want a Medkit, you can't give them an Arc Thrower, If you want a S.C.O.P.E. you can't also take a Frag Grenade, etc. Good News- it forces you to think ahead a bit on what you want each soldier to be able to do, and no matter how big a plasma cannon your engineers can build, the strongest weapon for X-Com is always your brain.