There's an extensive local bus system here, with marked buses and bus stops.
Having spent a lot of time on buses, and it being a long time since I lived there, I still don't remember numbers or routes. I'll see if I can get that information.
I've never seen bus maps in Mexico like you'll see in cities elsewhere. People find out which buses to take by asking around. Go to a bus stop and ask people there. Then, confirm with the driver. Some routes are very circuitous. Drivers don't mind letting you know when to get off the bus, and often other passengers will volunteer to help as well.
Of course, knowing Spanish helps, but just showing an address might be enough.
This company rents buses to travel in and around Monterrey or any part of Mexico at very reasonable prices. If you are planning to travel in a group (family trip, business trip, student trip), don´t hesitate to call them to rent a unit for as much time as you need! The owner, Mr. Jimenez, is really nice and he offers a very professional service. He was very happy to listen to what we wanted of our trip and tried to give us the best deal. I was very happy with the service. The buses are very clean and comfortable. The bus drivers were very nice and they drove us safely anywhere we asked them to. Highly recommended!
To explore Mexico simply take an autobus to go everywhere. Cost are cheap and is pretty safe to visit many states around Monterrey. I think companys as Futura, Transportes del Norte or Omnibus de Mexico are some of the best, even 1st class is not too expensive for most foreing people.
We went down to Monterrey by charter bus since we were on an orchestra tour.
Mostly, we just walked from our hotel, as it was fairly centrally located. Apart from that we just used the public bus transport.
From Laredo, a bus ticket cost me 13 dollars. The busses are very nice too. Much nicer than going greyhound. The highway to Monterrey is a nice tollroad so the trip only takes a few hours. If I were to go again, I'd catch the bus from the bus station in Nuevo Laredo and avoid the delays of crossing the boarder on the bus.
Inside Monterrey, there are many little buses to take you around the city and the most important and turistic places, ask in any hotel for tickets and routes.