How can I attach deck railing boards to the top of the rails?

Glue and Screw

Drill pilot holes from the bottom side of the lower 2x4 all the way through, Clamp the lower 2x4 in place and use 4 inch deck screws to screw up through the pilot holes and into the bottom of the upper 2x4 . ( 2x4 are only 3 1/2 inches ) so a 4 inch screw will give you enough thread to bite into the upper board just be careful not to drive them to far.

Screwing from the bottom this way will keep all screw heads hidden on the bottom side.

Apply OUTDOOR rated glue. Remove clamps.

Using your circular saw, cut a 3 1/2" deep and 1 1/2" wide notch off the ends of the 4*4. You may need your jigsaw to finish the deeper cut. The bottom 2*4 should fit neatly in this notch, fasten with glue and screws. Make sure these notches line up when installing the 4*4s. Then fasten the top 2*4 to the top using screws every 12" minimum. Glued in dowel could be substituted for screws if this is an interior application.

BTW, adding a corded drill, a 3/4" and 1 1/2" spade bit, and a 3/4" and 1 1/2" wood chisel to your toolbox would allow you an even more impressive range of joinery. You don't need a router or tablesaw for most classic joints, although they sure make it easier.

For all the decks I've built I've just use the same technique you'd use for the floor decking--screws from the top. Locate the screws in a nice pattern, and pre-drill near the ends of boards to prevent splits. I would probably put two screws at each end (into the post) and just a few in the middle. It won't take much. Set the depth precisely for best appearance--just a hair below flush.

You can spend time doing hidden fasteners if you like, but I wouldn't bother with glue. Outdoor glue only holds for a short time before it lets go, which means you end up relying on screws anyway.