I always recommend starting the follow up email with a positive statement. For example, thank the business contact for such an interesting meeting or for a successful negotiation or that it was good to reconnect with him/her.
Then, stay positive and say that it was good to reach an agreement regarding the topic discussed. This then should set the scene with the basic facts of the agreement. The real aim of the follow up email is to clearly write down all the points that you have agreed to with the business partner and that you want to higlight in writing so as to have the commitment of the other party in black and white.
If possible list the points for more visual clarity. Try and use language that is concise, coherent, not too complicated, explanatory and if necessary detailed.
Finally, at the end of the follow up email, thank the business contact for his/her commitment to the above points and tell him/her that if there is anything unclear to contact you at any time.
Here is an example:
Firstly I would really like to thank you for such an interesting day last week at your premises. I was really impressed when we toured your company and would like to commend you on such a smart business and with such a motivated and expert workforce.
During our meeting in the afternoon, we finally agreed on my company providing you with the following material and under the following conditions:
5 pallets of paper;
high quality paper in 165gsm;
delivery date between November 5th and November 15th 2011;
delivery location: your premises;
payment at 60 days after date of delivery;
payment by bank transfer.
I am extremely happy that we came to this agreement and would like to ask you to check over the details of this mail and to confirm your agreement. Please do not hesitate to contact me should you have any further questions or need any further clarification.
I look forward to hearing from you.