You need a US passport to travel to and from Mexico. It takes about 4-6 weeks, according to the US government, to secure a new passport AND to renew your old one (unless you pay a fee to expedite it, which is expensive).
If you have children under the age of 16, BOTH parents must be present when you apply for the passport. More info here.
You can find all the information on how to apply for a new passport or renew your expired passport here.