I've been asked to write this post (and feel free to keep the suggestions coming in - we love to know what everybody wants to hear) by the wonderful Nellie. And now that I'm feeling up to writing again, I'm going to tackle it. This is just the way I connect with Deity, but before I publish, I'll see what I can do to find other people's experiences. It is in no way the only "correct and right" way to go about forming a relationship with your Gods.
When I first started trying to "meet" my deities, I wasn't sure what I was doing. I've figured all this out by trial and error. This was about two years ago. I was researching the Norse Gods, and learning all that I could about them. (Keep in mind, that learning about your Gods really is a life-long endeavor. A lot of what was known back in ancient times was spread by word of mouth, and is lost to us now.)
There were a few Gods and called out to me. Eir was one of the firsts. In the long run I never really formed a relationship with her, so much as an acquaintance. Thor was a fairly obvious one, when I look at my life. And Frigg came along a bit later.
The first time I went to commune with Deity, I was trying to contact Eir. Having no training or knowledge of how to do this, I meditated and called Her name repeatedly. I didn't feel the presence of any higher being, but I "heard" singing. I knew it wasn't coming from my environment, because it sounded different than if I heard it with my ears. I never hear anything in my head (if it comes from me) in a voice other than my own. This was a very light and airy (Eir - pronounced just like air) voice, and a high soprano. I didn't catch the words, and I was so shocked that I got directly out of the meditative state and couldn't get back for the life of me. I tried!
Since then, I've formed relationships with Frigg and Thor, and I'm working on a relationship with Odin now.
My experiences with these Gods are more stable, and I can usually expect what's going to happen when I'm talking with them. The first time I started meditating to talk to these Gods, a location came to my mind instinctively. With Thor, it's an open field surrounded by trees with a large rock in the middle. When I meet up with Frigg, it's in a house, right by the hearth. And I see Odin standing by a cliff looking out to sea.
A (very vague) Guide to Connecting with Deity
Learn everything you can about your chosen deity. (Pick one or two to start off with.)
Meditate while "calling out" or "inviting" the God/dess to join you.
Take note of any feelings you get from them (if they come and join you - they might not.)
Be open to any kinds of messages you get from the Gods. It might not be in words - it could be symbols, sounds or impressions.
Don't be disheartened if things don't go as planned. You can always try again later.
Keep trying to commune with the Gods. They might want to be sure of your dedication to forming a relationship with them before they make themselves known to you. Patience is a virtue.
Don't forget to leave offerings or blessings for your Gods. A bit of your meal left out for them, pouring them some of your drink or just offering them thanks or praise before a meal is a good way to let them know you're sincere.