How can you contact dragons in the astral plane?
personally i just think of dragons and i'm there. i tend to visualize a field with a cave guarded by two dragons when i want to visit them.
What are some good books on the dragonic arts?
there aren't many actually, because most practitioners are secretive, and keep information within their clam [coven] but there's Dancing with Dragons and Mystical Dragon Magic by D.J. Conway [not recommended though, she's not the best source, however, she's credited with founding the path so you might want to pick up her books] there's also Sea Land and Sky by Parker J. Torrence though i haven't read that one so i don't know. been told it's good. then there's books about the history, mythology, and breeds of dragons throughout the world, but it's got little to do with Dragon Magick so i don't know if you'd be interested. [personally i feel they should be read]
How can you connect with your personal dragon?
While i have come across a spell, the better way is through meditation, and projection. when you are ready, your Guide will reveal himself. the Guide dragon usually stays in the astral. your Guardian dragon is a young dragon that normally stays in your house to protect it from danger. they typically tell you they're your guardian, and just appear one day. dragons come and go much like spirits and other astral beings, but your Guardian and Guides will tell you who they are, and will stay for life.