On the Docker EE page you will notice 11 available editions to choose from.
Select your preferred edition, and you will be redirected to a page specific for that edition. This page includes a description of the edition and also includes a link to start a 1 month trial.
Click the Start 1 Month Trial button, select the account/organization you would like to associate the trial with from the Subscribe as dropdown menu, enter contact information, click the I have read and agree to Docker's Software Evaluation Agreement checkbox, and finally start your evaluation.
Your trial will be available to you from the My Content page of the account or organization you associated it with.