Sure it is surface mount technology. You do have to be careful to not provide too much stress, as you can pull off the pad.
You could just solder wires to the pads.
This pcb allows you to solder a surface mount header and a pogo pin to your teensy, and then use the bigger board on a breadboard or soldered to a perfboard:
https://www.tindie.com/products/loglow/teensy-31-breakout/?pt=full_prod_search. If you are unsure of your soldering skills, and need the pins attached badly, you can order a Teensy that is pre-soldered for about $60.
This is an easier way to solder pins to the underside of the board than using a SMT header:
https://forum.pjrc.com/threads/26071-Using-all-Teensy3-x-pins-with-a-socket
This is another board that provides an Arduino style shield mounting as well as additional pins from underneath. Like the first item, you can order a Teensy pre-soldered. I don't think this board has provision for the reset pin (in Teensy 3.0, the reset pin was on the back, in 3.1 it was in one location underneath the pcb, and in 3.2, the reset pin moved):
https://www.tindie.com/products/freto/teensy-3-breakout-board-and-shield/?pt=full_prod_search
This is a 3rd board for accessing the underneath pins. You can order 3 of these boards from OSH Park for about $8.30. Unlike the previous two boards, you don't have to solder a SMT header to the underneath pins. Instead it is meant to be installed directly under the Teensy, and you connect the underneath pads with a bit of solder.
Note, I haven't yet done any of these. I was going to do the last one, but my soldering iron looks like it is giving up the ghost, and I may need to replace it. I have the other two boards, but so far I haven't attempted soldering the SMT headers.