Buying private medical insurance over the internet is a simple process, you will just need to provide your credit card details, your permanent address and contact info, and then you will receive you policy document by e-mail.
Pay attention to what your policy will actually cover before buying. Do you intend to do winter or water sports? Do you have any illness or disability that needs to be declared? Such factors will affect the overall cost of your policy. Once your policy document comes through keep it in a safe place and always have the emergency telephone number of your insurance company and your policy number on your person when you travel.
Check with your credit card company before going: some credit card companies offer travel insurance if you use their card to purchase the flight.