There’s a lot of hulabaloo in the pagan community revolving around patron gods and godesses. People who are new might be anxious to find out who their patron is, because so many seasoned people talk about their relationships with their patron deities. But the thing is, nobody gets helped by rushing things and trying to find a god before they want you to find them. You might not even have a patron in the first place, and that’s okay.
Try to find a pantheon that you feel drawn or connected to at first. It doesn’t matter if you’ve heard of them from media or not. For instance, I first heard of Amaterasu from the game Okami, and our relationship has worked out fine–the game was just a means to an end, the same thing goes for Marvel’s Thor. It doesn’t make you a fluffy bunny if you hear of a deity in media.
Once you’ve found a pantheon or multiple pantheons that attract you, do your research. Find holy texts, legends, etc. for that deity and read. You should also look at others who work with those pantheons and what they have to say about those gods. Finally, open yourself up. Communicating with a new god usually should start with some kind of libation and prayer, since you’re basically sending out a signal that says ‘hey! Look at me!’. Not to mention, the gods dig libations.
As for watching for signs, if you don’t have a very good godphone, you can use divination; pendulums, tarot, runes, etc. can give you hints if the god or goddess you’re looking for is trying to contact you. You could also try astral travel. (Although caution should be used on the astral, as spirits could masquerade as gods in order to deceive you.) I can pick up feelings and even snippets of words on occasion when a god is particularly close or I’m in meditation. However, the conversations-with-the-gods thing isn’t as common as people make it out to be. Usually, it’s gut instinct, astral, omens, divination, or a combination thereof. Getting a complete picture of what a god is trying to say can be difficult, but it’s usually worth it.
Forging a relationship with your god or goddess, or gods/goddesses, is important. Gods are not your personal slaves or entities you come to when you need a favor. What you should want to do is please the gods and serve them, and form a relationship with them. Some people prefer to have a professional relationship, where one isn’t exactly ‘worshiping’ their patron but ‘working with’ them. I worship my deities, and I humbly ask for their assistance on occasion; forging a relationship with a god is kind of like forging a friendship: You have to maintain it, otherwise, it’s for naught.