First of all, make sure that the soldier actually got some kind of grenades in their loadout. When they do, you can throw grenades with the grenade icon in the HUD:
- (optional) right-click on the picture with the grenade to switch the type of grenade you want to throw. Select the type with left-click.
- Left-click on the grenade picture to enter throw mode.
- Move cursor on the map location where you want to throw it.
- Check if you have enough time units left. When the TU number next to the cursor is red, then you won't be able to throw it. Throwing grenades requires more time units than firing most weapons.
- (optional) laugh manically and shout "Die, alien scum!"
- left-click to throw.
- (not optional) Curse, because the grenade flew against an obstacle and killed your own soldier. Oh, did I forget to mention that grenades use the accuracy mechanic and don't always land exactly where you want them to? Sorry about that.
By the way: When your soldier has a free hand (most weapons are two-handed, though), then you can put a grenade into a free hand-slot and throw it just like you would fire a normal weapon. But there is no point in doing that. Moving the grenade to the hand-slot takes additional TUs, but the TU cost for throwing from the off-hand is exactly the same as throwing from the belt.