How do I use the sword and shield I found?

It sounds like you might be on your Inventory screen rather than the Equipment screen, which is where you need to go to equip gear and set your quick-access items. Does the screen you're looking at look something like this?

If so, you want to use RB/R1 (or your controls' equivalent) to switch to the Equipment screen, which should look like this:

From this screen, you can select the slot that you want to equip something to. From top to bottom, left to right, those are: weapon (2), shield or off-hand item (2), armor (4), quick-access items (5), arrows (2), crossbow bolts (2), and rings (2).

If you have multiple weapons or off-hand items equipped, you can switch between them using Left and Right on the D-pad (or your controls' equivalent) during gameplay.