When you divide 161 by 7 in long division, you start with the first 1 (representing 100), which you cannot divide so you stick the 1 in front of the 6 and then divide this number (16) by 7 which gives you the remainder 2. With this remainder you put it in front of the 1 (the third digit) to get 21. this then divides by 7 three times to leave no remainder.
If the original number was 162, at this point you would get a remainder of 1. If this is the case, to turn this into a fraction all you need to do is divide the remainder by 7 which is something like .143.
I hope that makes sense. Here is a crude representation of it. It’s hard to describe over the internet without showing you the processes that I have done, but with the above text I hope you can figure it out.
http://img256.imageshack.us/img256/1425/longdivision.png
As for the final part of your question “what does this last sentence mean” I am unsure what you are referring to. If you are referring to “and writing the result in the tens place of the quotient.” this is the third step in the image where you put the 2 in front of the 1 to get the number 21 which you then divide by 7. In the first/second step what you are really dividing is 160 instead of 16, but in shorthand you just write 16 else it gets messy, especially with larger numbers.