You have two ways to go:
1) You marry her, she goes back to Mexico, you file the I-130 requesting her as your spouse and she goes through consular processing in Mexico.
2) You marry her, she stays here (even if she overstays it will be forgiven), you file the I-130 & I-485 (along with the supporting documents and forms). So she would be adjusting status and her status in the US would be pending until the petition is approved. You can file for I-131 and I-765 for her to be able to travel (if she does not overstay) and work legally.
I would advise against filing for an extension, because for a tourist you will require a strong valid reason to stay. Staying because of marrying an US Citizen at some point is not a valid reason, in fact, it is very likely going to be denied and she will be requested to leave the country within 30 days.
Also, she can not work here legally under a Visitor visa. (Unless she applies to change status, which is another process).
The easiest choice would be choice # 2, for as long as she can overcome the 30-60-90 rule. How long has she been here in the US with you?
Time frame, depends on several factors... You are looking at 4-8 months with choice # 2 (adjustment of status) if it all works out well. And 6-10 months with choice # 1 (consular processing) again if it all works out well.
I advice you to read the stickies on this forum. Specially here:
http://www.immigrationportal.com/showthread.php?t=188386
I hope it all goes well for you guys.