This is not an easy topic. I'm going to do my best with it, but there are many things that are either personal or private to my experience with a God or Gods: things I might share one-on-one with a friend, but not on a public blog. I do think the topic is a vital one, regardless. What could be more worthy of consideration than the very experience of the Divine? The usual caveat (see Communicating With The Gods - Part I) applies with this post: I am writing from my own "jurisdiction," from my own "precedents," and can speak only to my own experiences.
Our society is pervaded by certain underlying, almost subconscious approaches toward Holiness that can be absolutely useless in a Heathen context. For example, one of the subtle influences of monotheism is the "thou shalt not test thy god" attitude: that is to say, asking for a regular confirmation of a divine presence(s) is a "bad" thing in some other faiths--or at least it is perceived as a bad thing. Mystics of all faiths step outside this view, of course.
It was brought home to me that such "testing" is not an issue with our Gods. Not with certain Ones, at least.
I'll give a real-life example of just how contrary to our preconceptions the experience of a Divine presence can be. However, first I need to back up a bit. Long story short, I've been comfortable with sensing energy for about a decade (a Neo-Pagan coworker once suddenly handed me off a ball of energy during a commute home--"here, catch!"--and thus jolted me out of my Atheism). I gather some folks can "see" this energy; I just sense it as a sort of invisible tension or pressure in the air. Since then, I've played around with the natural sort of energy one can call up in one's hands. It was an interesting sensation, but I didn't see much use for it overall. That kind of energy only has so much strength to it. It comes from within and seems to reach a plateau much like any other sort of human energy. But being sensitive to it has been invaluable in other ways....
Holding Out A Hand
One way I experience the presence of a God or Goddess is by, quite literally, holding out a hand or hands and feeling the responding touch. This can be interesting, giving you a new, very immediate sense of the God or Goddess that goes outside the realm of meditation. But how does one do this?
I tend to start with meditation, i.e., I attempt to visualize the God or Goddess to in the mind's eye, mentally call Him or Her by name, and see if the God or Goddess wants to chat. Some responses are highly enthusiastic; others might give you a polite, distant nod, if that much. Sometimes, the timing simply isn't right with a God or Goddess you may connect with deeply later on, or maybe your personalities might not be the best match. There are many levels of friendship and connection.
If you get a welcoming response, you might try holding out a hand. Actually, this started off for me at the request of one of the Gods. You might get a brushing of the fingertips... a soft touch from a Goddess or a firmer grip. I found Loki's touch to be a rather initially disconcerting, but strange and fascinating experience, the first time. Not unlike the God Himself.
Another way I've experienced the Presence of a God or Goddess is through meditation, but the meditation ascends into a flowing sense of "light and height." Since Odin is the God of Wisdom, I don't think He will mind me sharing an impression received of Him in this way: I began to feel "lifted up," like being a thousand feet tall, with a sort of powerful gray-white light in the mind's eye. Somewhat amusingly, I also started to feel like picking a fight with Him, for no sane reason whatsoever: Odin is also the God of War.
A few final notes. Presence can't be forced--it is Their gift to us--but it can be helpful to mentally offer more "formal" worship to a God or Goddess who wants to connect with you while They are attempting to do so, e.g., titles, attributes, deeds, etc.--whatever comes from the heart. Physical offerings can also be helpful at times; it is nice to bring a present on a visit, especially if you don't know someone very well yet. But, getting back to what was written above, it is very possible to have a daily or even more constant sense of presence where one has a friendly relationship. Some of the Gods, at least, are only a thought away, if not closer.
I've noticed there can be misunderstandings at times, as discussed in Part I. Patience and a willingness to try again are important. There are also natural human limitations that can and do interfere with connection. Falling asleep is a real problem for me; I work bizarre shifts. Fortunately, the Gods seem to very much understand. They have a great deal of patience--so long as one tries to be halfway respectful, at least--and quite a sense of humor.