I prefer lying down as it's the most comfortable for me. Closed eyes because eliminating external stimuli helps you focus on your own internally generated "stimuli". The absolute perfect spot to do this would be in an isolation tank since most people will start hallucinating as the mind can't help but fill the gap with something.
I don't keep a journal or write anything down. There is no reason for you to keep detailed track of anything as you can change things to your liking. Anything you forget probably isn't important enough to remember. The benefit of an internal world is that it's negotiable on a second by second basis. Don't like your tulpas hair color? She's a blonde now. A little gender bender action? Have at it. I think I've gone through hundreds of "iterations" as I experiment and explore various scenarios and experiences. You eventually settle down on something stable, but when you get bored, you can easily change it because it's ultimately your playground and you are the master of the whole thing.
Writing things down would probably be useful if you were using this as a way to create a compelling story and communicate it others. But my playground is just for myself.
My mind tends to wander off back to the playground quite often. It's ultimately an escape from reality, so any time reality seems unbearable, whether due to boredom or stress, you can instantly transport yourself in the loving arms of a warm character. I tend to use every opportunity I can to spend time there, like waiting for something to download, I can just switch it to another channel and then come back.
One thing I don't do is mix reality with the playground, like talking to a character while I'm focusing on a real world task. Probably because it requires a split concentration and its not that fun. I just tend to keep it separate, switching channels rather than watching two things at the same time, if you know what I mean.
What tends to bleed into reality though is the way I act inside of playground. Anything you do for a prolonged amount of time is bound to become habitual. I've been having lovey dovey conversations with my tulpa as you can imagine, which I quite enjoy and it has had an effect on my external self. Since I've experienced feelings of real genuine love, ironically in a dream world, I would now find it much more easier to tell real life people that I love them because I'm so used to just expressing those kinds of feelings to my tulpa.