I recommend the Keirsey Sorter II found on the internet. The same personality profile test is on Facebook, and it is called MyType. Both give you four letters. INFP or ENTJ, that sort of letters. The test will give you an explanation of the letters. Be sure you save the percentages. For instance, a 9/10 introvert will have much different needs and choices than a 2/10 introvert.
With the Keirsey Sorter II, you will receive a printout telling you your degree of four different personality patterns. There are two books to help you understand the letters: Please Understand Me-Character and Temperament Types by David Keirsey and Marilyn Bates' Gifts Differing-Understanding Personality Types by Isabel Briggs Myers.
Have fun finding out about yourself and your partner. Don't take yourselves so seriously. Utilize those differences. If you were a business, it would be beneficial to have someone good at customer service, and the other an expert accountant. In a romantic relationship, those differences can also complement each other. Let them!