Your journey from the Lisbon Airport to the city of Braga will likely pass through the "Estação do Oriente" ("Orient Station") train station. This page describes how to get there, how to buy your train/bus ticket to Braga and get on it. It also describes one or two alternatives.
This is what you're expected to see when at the airport.
Get outside. You can easily catch a cab if you want. Well, actually, there's usually a big line to catch cabs, but I'll tell you a secret: If instead of getting out of the airport through the door you see in front of you you turn right, walk up the escalators and get out the door there, you'll see lots of cabs waiting for you. People are just waiting in the wrong line...
Here's what you do to catch the bus you want, but also read below to see the bus schedules. At some times during the 24 hours of the day, you'll really have to catch a cab to get where you're heading next.
Cross the street.
If you happen to see some policemen and need information, those are the guys to ask. They can be very helpful.
Keep on moving.
You're almost there, cross this street and turn right.
It's right after the yellow car (it might not be there then, though).
Cross this street.
You can already see it...
There! You've only walked about 100 meters.
You'll see this plate on top of the bus stop.
You want to catch bus number 5, and get to either its penultimate or last stop.
Be sure to also read LisbonBuses, for a better understanding of how buses in Lisbon work.
Bad news: this bus doesn't run on weekends nor holidays, and the first one is at 07:00 and the last one at 20:40.
Good news: there's another bus you can catch during the night! The is bus number 208, and it will take you to the same place.
This one runs from 00:30 to 05:35, all days (er... nights).
Get on the bus. The ticket costs 1 euro and 20 cents.
You want to go to the "Estação do Oriente" ("Orient Station"), but there's no need to tell that to the driver. With these buses, you just get in, pay, and get off where you want to.
The place you're heading too can easily be distinguished by the rooftops.
This is the bus stop you want to get off at, but...
...the next one (and last, too) is just 100 meters away from that one, so don't stress :-)
Again, be sure to also read LisbonBuses, for a better understanding of how buses in Lisbon work.
Now that you're here, you might want to have a look at the map provided by the Subway site.
If you got off on the first of these two stops, pass this corridor and then turn left.
You want to go up these stairs.
Here you'll find the place to buy tickets. Notice the machines on the left and the lines on the right.
If you want some human interaction, either buy your tickets with the humans or start a conversation with somebody else around.
The machines have an option for some other languages, including English. They also take Visa. They are usually faster, as the lines tend to be smaller.
Regarding what train to catch, you'll find a schedule around.
The trains "Alfa Pendular" and "Intercidades" are the "fast" trains that might get you there. You can find the schedules online here. You will notice that, during the day, there are only three trains in that list that will take you from Lisbon to Braga. As alternatives, you can take a train to Oporto and from there another train (or taxi) to Braga.
AN IMPORTANT NOTE ON THESE FAST TRAINS: Tickets for these trains can be bought in advance, but not from out of the country. There's usually no problem with having tickets available, but there might be, especially if it's a Friday, so here's a couple of tips:
In the eventuality that you can't buy a ticket, here are some alternatives:
Departure: 00:15 h Arrival: 04:45 h Frequency: Mondays (or Tuesdays if Monday is a holiday), Saturdays (or Fridays if holiday)
Departure: 00:15 h Arrival: 05:40 h Frequency: Everyday
Departure: 07:00 h Arrival: 11:30 h Frequency: Everyday
Departure: 08:30 h Arrival: 13:40 h Frequency: Everyday
Departure: 12:00 h Arrival: 16:55 h Bus change at 15:45, in PORTO Frequency: Everyday
Departure: 13:00 h Arrival: 17:30 h Frequency: Everyday
Departure: 13:00 h Arrival: 18:10 h Frequency: Everyday
Departure: 15:00 h Arrival: 19:30 h Frequency: Everyday
Departure: 16:00 h Arrival: 20:40 h Bus change at 19:30, in PORTO Frequency: Mondays, Tuesdays, Wednesdays, Thursdays, Fridays, Saturdays except holidays
Departure: 16:00 h Arrival: 21:10 h Bus change at 20:00, PORTO Frequency: Sundays (or Mondays if holiday)
Departure: 16:30 h Arrival: 22:10 h Frequency: Everyday
Departure: 18:00 h Arrival: 22:30 h Frequency: Everyday
Departure: 18:45 h Arrival: 00:10 h Frequency: Everyday
Departure: 21:00 h Arrival: 01:40 h Bus change at 00:30, in PORTO Frequency: Sundays (or Mondays if holiday)
I don't know anything about the amount of passengers these buses get, so I can't tell you anything at all about the seat availability. However, they certainly seem to have a lot of buses...
The bus ticket from "Rede Expressos" from Lisbon to Braga costs 15 euros.
The rest of this guide assumes you managed to buy a train ticket.
Buy your tickets.
They cost up to 39 EUR. Notice that you might need to exchange trains at Oporto. If so, somebody is likely to tell you so, but it doesn't hurt to ask the person who will check your ticket on the train.
If you have some time to linger, know that there are some stores on level -1. Level -2 is where you catch the subway.
If you have even more time to linger, you can cross the street and go the Vasco da Gama mall. It's a very nice mall.
Afterwards, go up the stairs to catch your train.
This is what the lines look like.
And you'll be able to see something like this on the right line.
The train from Lisbon to Braga takes about 4-6 hours. See you in Braga.