(1) A bit of mechanical knowledge with bikes is a good thing, but as you say
learning about it in the cold is not the ideal method.

(2) I'd be very surprised that a bike shop would fit a chain ring etc. without
checking the gear action, although perfection is sometimes hard to achieve
without a trip or two on the road.  Therefore I'd ask how you transported the
bike between home and LBS.  If this involved stuffing into back of car or
manhandling onto roof rack 'something may have been bashed'.

(3) How it works
(a) There's a 'puller' marked 1-2-3 on the handlebars...
(b) ...connected by a cable...
(c) ...via a cable guide (flexible tube) and often a cable guide
     (saddle-shaped groove) on bottom bracket...
(d) ...terminating in a cable clamp on the actuator arm.
Pulling more on the cable brings the actuator into the frame more which
drags the chain onto the lower gear ring.  And vice versa.

(4) Why it doesn't work in your case
(a) Either there isn't enough pull getting to the actuator
(b) Or the actuator is prevented from moving enough.
To see which of (a) or (b) is the case you turn the bike upside down,
crank the gears round by hand and pull on the exposed gear cable
running up the bottom tube.  If you can get the gears to go into
bottom then the problem is (a).  If you feel the actuator getting
to some mechanical obstruction then problem is (b).

FWIW I suspect your problem is (a).  The puller may have got
knocked during transportation or the cable may have jumped
out of the vee-guides.  You should be able to fix this
at home.  You may need to 'shorten the cable' by releasing then
retightening the cable clamp on the actuator with more 'end' spare.
Work out how the little knurled adjuster works on the puller and
get this /fully/ into your head so you can make small adjustments (which
are generally necessary to get perfection across the whole gear
range) on test rides. (One way to do this is to twiddle the adjuster
with one hand while your finger is on the actuator.  You should be
able to feel the actuator move.)

Some not so good news.  If the chain hasn't been changed be prepared
for some jumping when under power.  It is generally reckoned to be
a good idea to change the whole bloomin' lot all together (front, rear
and chain.)