This is the best site I’ve seen on how to/which buses to use to get around Istanbul. You can also use the cities site, click here, but I’m not a fan of it since It doesn’t tell you how to get from one side of the city and which buses to use if you need to change. You have to first know where you’re going/starting from and as a newbie…that’s impossible.
Also, traveling by bus to get from anywhere within the city or cross-country is the way to travel here. It’s cheap and the buses offer some refreshments and a stop ever 3-4 hours. The buses are either 1 seat then two side by side on the opposite side of the bus; or 2 seats per side. Don’t sit in the very front or back or just behind the door because there is NO leg room. (Or maybe I’m just tap). You can check http://www.obilet.com for all buses going/coming from where you need to go as well as the times and availability. NOTE: Turks will NOT place opposite genders next to each other on a bus so don’t even try. If you have a lot of bags don’t worry, they’ll stow them under the bus and give you a little ticket for free. You can put smaller items above you on the bus. They usually offer headphones.
Metroturizim (I’ve heard Turks don’t like this company as much anymore because of some embezzling bust a few years back)
Nilüfer (I prefer this one)
This of course is not all of them, but it will get you started. Some of the companies are regional or city oriented (inci for example is a Kayseri bus)
You don’t have to buy your tickets online either. You can go into any shop, ask if they have a bus to your destination and pay right there. They often have free shuttles too so you should ask if they don’t tell you or it’s not in front of where you are.