Dear Mr./Ms. Last Name,
Thank you for taking the time to talk with me today. Express your gratitude for time spent with you, advice, etc. in this area.
In this area, express your thanks for any specific advice given or recommendations, such as potential job openings or their efforts to connect you with networking resources that may assist you in your search for employment. This is where you would thank a prospective employer for granting you an interview as well.
Here, let the recipient know that you would welcome any further advice, and that you will let them know the results of their efforts.
In closing, express your thanks and appreciation once again.
Of course, when writing an appreciation letter to a friend or relative you do not have to write in a formal manner. The example above is geared more toward a business-oriented appreciation letter.