As in any relationship it's reliant upon communication and listening. I agree with what others have said about thinking of Him as your friend and just talking to Him like he is. I will just start talking to Him while I'm doing laundry, washing dishes, cooking dinner, etc. I talk about how I feel, and things in my life, just about everything basically.
I know someone who said that throughout the day they would say, "Lord you're here and I'm here". They said it keeps them feeling close to Him and reminds them that He is always with us. It's also important to read the Word daily. That's how we learn about God...who He is, His character, etc.
It's not just talking to God, it's also listening. We need to have quiet time with Him that we may hear what He has to say to us. The way I do this is by going to my room, grabbing my notebook and pen, and sitting quietly. I will say, "Speak Lord for I am listening, ready and willing to obey." and then get quiet and just listen for that still, small voice of the Lord. I keep a notebook that I write everything in.
I like the idea of writing a letter. I've never done that before, I always just start praying, talking to Him and just write down what He says, not what I say. That's just the way I prefer, but I think a letter is nice. I do believe that you can receive an answer to your letter, you just need to get quiet and listen.