How and when to consider 面子 when speaking Chinese? Avoid Losing Face ( 沒面子 )

As a student of Chinese I would like always maintain a respectful tone. It can be very easy when speaking a second language to make mistakes that offend others. I would like to avoid such experiences as much as possible. 

Normally in class, students are taught the basics such as:


  qǐng wèn 請問 and nín  您


Having these two phrases only, does not appear adequate to someone who wants to begin speaking to Chinese people. I am hoping readers can share additional language experiences, structures, or words that would help me to avoid making the other party (or myself) lose face. Specific grammatical phrases that help soften or smooth over any mistakes would also be helpful (like 對不起, etc.).
A mistake I make often (but sometimes it's kind of fun) is connecting peoples names to bad things.

Like:

A: 我姓刁。

B: 哦，是刁难的刁，对吧？

People seem to be kind of offended by this kind of stuff. Try not to connect it to 'bad' or 'negative' 'non-positive' things.

edit: oh yeah - also don't use 以小人之心，度君子之腹 with people [that is including the person you are talking to into the saying] even if you think it's a perfect fit for the situation - people will just assume you are calling them a 小人...