As a Marketing Cloud Administrator launch the Enterprise Dashboard https://adminconsole.adobe.com/enterprise/
Learn how to access DTM through Marketing Cloud
Navigate to Products tab, and select Dynamic Tag Management product.
To add a configuration, click the + icon on upper-right corner.
Name the configuration (as per your requirement, for example, DTM Admins)
Under Permissions, select "Admins" from drop-down and "Save" the configuration.
Next, navigate to "Users" tab, and select the user (who needs access to DTM).
Add the above created configuration to the user, and "Save".
Similarly, you can gain "Approvers", "Publishers" or "Approvers + Publishers" access in DTM by creating a configuration for each of them by following the steps 1 to 5 above (Choose the required configuration in place of DTM Admins as per the case).
This is for DTM accounts that were created after April 5, 2016:
Here's a link to the documentation, similar to the steps above:
If the above steps do not work, try the following for legacy DTM accounts: