How can I cut/route a small, straight slot through a piece of wood?
Use a router with a plunge base and either an edge guide or straight edge, depending on the size of your work piece.  Attach stop blocks to the workpiece and/or straight edge (clamps would be one easy way to hold the stop blocks in place).  The stop blocks will prevent you from cutting your slot too long.  First set up the edge guide or straight edge with the appropriate offset for your router base, parallel to where you want the slot.  With the router unplugged and the bit almost touching the wood, position the router bit where you want the slot to start.  Then use the router base to gauge exactly where to position the stop and clamp it in place.  Do the same for the other end of the slot, then proceed with plugging in the router and cutting the slot in several passes, going slightly deeper each time.

You can also use a router table to do something similar, but the steps for setup will be different since you won't be able to see the cut as you're making it.  However, you will be able to use your router table's fence and possibly other T-track or miter track accessories.

Although your material isn't very thick, it's still not a bad idea to cut the groove in multiple passes.

In a pinch, you can also use a Dremel/rotary tool (which is essentially just a tiny, low-torque router) along with a router attachment and multipurpose spiral bit, but a router will give you slightly better results.

If you don't have a router, it's relatively easy to cut this slot by drilling a series of overlapping holes with a drill press and Forstner or brad-point bits, then clean it up with chisels.

No matter what solution you use, be sure to put a sacrificial piece of scrap wood on the back side of the workpiece to help prevent blowout when you cut all the way through to the other side.