The ethereal beings you are referring to as dragons don't often appear as guides specifically to people so if you specifically want help from them you could try calling one or evoking one.
Of course astral projection is a possibility but still unnecessary.
This is a great question and I actually suggest the most basic of all practices, meditation. Meditation assists you in settling your mind and focusing staying open to what you experience. Besides that it's all you.
trying to remember correctly, automatic writing, meditate with a pen and paper, when you get into a trance state, your guide might appear and begin moving your hand and write/draw things. don't quote me, it's been a while since i read up on it, look it up in google, it should come up.
a spirit guide along with a dragon guide isn't something you make a chant for and it appears, it takes patience. spirit guides will come to you when you need help, many cultures it take years of dedication, spirit/vision quest, and various other coming of age ceremonies where you study, and/or put your body into extreme situations for your mind to open and find your guide. just meditate, think about aspects of yourself that hold some significance, if you feel drawn to a particular place [a tree a bench a lake] go there and meditate.
with dragons, it's hard. dragons were betrayed by humans so they're leery of us. it takes a long time to gain ones trust. you need to preform the Entering the Dragons Cave [mouth] ceremony, which is a self dedication to them, to let them know you wish to learn. you don't need to project, you can call them forth to watch as you would the watchtowers and Lord and Lady in and regular circle, or you meditate and visualize the whole thing on a sort of guided meditation. it's not AP but it'll work the same for the ceremony. after you complete it, the dragons will begin to visit you, and figure out if they should teach you. eventually you will get a guide.