As others have said, you mention anything you think is relevant to your claim, and you don’t have to have a diagnosis to claim. It may be helpful if you do have any medical evidence, to send copies with the form.
Applying on mental health grounds alone is much more difficult because generally these types of claims are held to a higher standard to meet the elgibility. When you get the application form there will be a date on it by which you must have the form returned or your claim will time out. Can I suggest that when you get the form you ring DWP on the number that will be on the covering letter, and ask them for an extension to this date - they have discretion to give you up to a couple of weeks extra. Tell them you want to use this time to gather evidence and seek help on completing the form. Medical evidence is useful if you have it, but you can also ask for others who are involved with your condition - either in a professional capacity or friends/family who know you well and support you - to write a short description of who they are and how they help you.
While you’re waiting for the form to arrive, it would be a good idea to contact an agency like Turn 2 Us or the CAB and ask for help in completing the form, as the questions are easy to misinterpret and can trip you up.
Also when you send back the form along with any evidence, if you can afford it, it’s wise to send it back to DWP in the envelope provided, but send it by special delivery and keep the receipt until DWP confirm that they have received your application. DWP won’t accept any other proof of posting such as the free certificate of posting issued by the post office, because their policy is that proof of posting is not proof of receipt, so you need to use a service which tracks the delivery and asks for a signature on receipt.