Hit f1 to open up your stat page then in the bottom center of the page hit the "Next Page" button. Now double click on the claymore you picked up, now it should be highlighted bright yellow, now it should be equiped.
Press esc, then esc again to exit the inventory/ stat page. To swing hold the right mouse button and move your mouse in the direction you want to swing.
Don't give up on this game until you get out of the first dungeon, its quite tough for a first one.