More commonly referred to as your Guardian Dragon, and you do not "summon" it either. Summoning is done to bring forth a spirit for work or to serve you. Dragon energy serves no man, but can and will work with you in your daily life, and magick practice.
Most common way of making contact is through meditation. You can visit the Dragon realm through AP but not required to find or ask to meet your Guardian/Companion. Clearing your mind of all things, and focusing on your desire to make contact is all that is required. Though some people like to speak out loud which is ok as well. Be patient, it takes time.
Throughout your practice you can come in contact with many different Dragons, each may only stick by you for varying amounts of time, each teaching you something different or building upon knowledge you already possess. As for what is like, when you do meet one you will know for sure that mankind is not alone, nor the biggest presence in the world.
Be sure to be polite and respectful. Being disrespectful at all towards any Dragon entity or energy will result in many unlikeable ways and including being shut off from their presence.