If you are looking at Olson Park from a birdseye view, you can find the entrance along the south side of the park, about halfway in between each side of Olson Park. A map can be found on their website. You can most easily find it by looking in between the basketball court and the soccer fields.
Although this park is open to the public, Ann Arbor does have some rules and regulations. For all the dog parks located in Ann Arbor, your canine is required to have a permit from the city. To acquire the license you will proof of vaccination records, verification they are spayed or neutered, and a waiver of liability to protect the town from any harm that could come from canines at this park.
There is also a fee associated with the annual permit. The costs can change by how many canines you have as well as how many of the cities parks you would like access to. If one dog and just the Olson park, you can get the pass for as little as $25 per year. To access all the parks in Ann Arbor, it is a $60 annual pass. Your canine can obtain this permit if they are not spayed or neutered but at an additional cost.
You can get a copy of the application on the Ann Arbor website (the link is below), and you can bring in the completed form to the city clerks office to get a permit. You can also mail in your application with a check, the address for mailing is listed on the application.