The best way to get around in Mexico City if you don't know the local bus system is definitely the metro. It is the second largest metro system in North America after the New York City Subway and you can get everywhere for only 5 MXN (about €0,25).
When you enter a station you can get a ticket at the 'Taquilla' for 5 MXN per person per ride. You can also buy a rechargeable card for an initial cost of 10.00 MXN. Then you can recharge it for a couple of rides so you don't have to wait in line every time. Every ride still costs you 5 MXN, it's just for you convenience. We always bought seperate tickets because most of the time it only took about 1 minute to get a ticket, but one time we had to wait in line for 15 minutes!!! Advantage: we could get a pizza slice (not the best I've ever had but still descent) while waiting for only 15 MXN (about €0,75). Love all the booths that sell food in the metro!
All lines operate from 5 am to midnight weekdays, 6 am to midnight Saturday and 7 am to midnight Sunday and holidays. Platforms and cars can become really crowded during rush hours (7h30 am to 10 am and 3 pm to 8 pm). At these times the forward cars are reserved for women and children, and men may not proceed beyond the ‘Sólo Mujeres y Niños’ gate.
Always be aware for pickpockets under the ground! Especially during rush hours and at the more touristic stops for example Zocalo. We know what we are talking about because we also had a miner issue (luckily we could take our phone back out of their hands). The way they mostly operate is by forming a big crowd around you and pushing you into the metro car. In the meanwhile one of the group will try to steal your wallet our phone out of you pockets and runs away while you are stuck in the metro car. If you can, always put your belongings in your backpack and wear it in front of you. Otherwise hold your hand in your pocket with your phone/wallet so they can't take them. Don't give them a chance!