Colombia does not have a government-run post office system. However, the private firm 4-72 serves as Colombia's de facto postal service, though it tends to be somewhat slow and unreliable. Locals rarely use the 4-72 service and usually go to couriers such as Servientrega, which have many more branches than 4-72, though they are very expensive when used to send mail overseas.
It's simple enough to get a SIM card and even an unlocked phone at the international airport in Bogotá, although there is, of course, a price hike. They're not hard to find in any city either, just ask your hotel or hostel staff where to go. Topping up is also easy, and can be done pretty much on any street corner.
The carriers you'll most likely see are Claro, Tigo, and Movistar. Claro is the most expensive (by a little bit), but has the widest coverage in the country, if you expect to get off the beaten path.
Virgin Mobile might be the best option if you want to have internet for a low price, as you can pay for COP$20000 for a month and get 350MB (plus 50 minutes, 10 sms and unlimited use of WhatsApp, an almost universally used chat app in Colombia) without the need of a contract. It might take a bit longer to find a spot that sells the sim cards. It should cost COP$5k-10k pesos.
To call from a landline to another local landline, dial the normal seven digits. To call from a landline to a mobile, dial twelve digits, always beginning with 03, followed by the ten digit number provided.
It's far more complex to make long-distance domestic calls or international calls. Ask whoever owns the phone to dial it for you. If that's not an option, buy a mobile phone. Seriously.
From mobiles and from abroad:
To call a Colombian landline from another country or from a mobile phone in Colombia, use the +57 country code then the eight digit number (the first of which is the area code). To dial to a mobile phone, dial +57 and then the ten digit number. You can also type "00" instead of the "+".
Internet cafés are easy to find in any city or town. Expect rates to run about COP$1,250-2,500 per hour, depending on how much competition there is (i.e., cheap in Bogotá, expensive in the middle of nowhere). Quality of connection is directly related to the centrality of location, and hence inversely related to price.