I can describe how a transition usually is experienced by me and perhaps it gives a more clear picture of how it can be like.
Remember though that only see this as inspiration not fact, the best source of knowledge is your own experience.
I will describe a transition from a DEILD.
I wake up and realize that I have woke up, I look at my alarmclock and I write down the time of my awakening. I see that it is still night and that it is to early to get up.
I notice that my awareness feels a little different, sort of like a dream feels, a bit hazy and well it's impossible for me describe what I feel, but you will now what I mean if you feel it, it's a different awareness than usually anyway. I then perform a reality check to make sure that I am not dreaming.
Then I choose a comfortable posture, usually on my side and I start daydreaming, the different awareness somehow makes me my visualization get life on it's own, I don't control exactly what I think about, I mgiht think about walking around my house, but it gets filled with random things. Like sometimeI might see a random woman walking around and sometime I might see a giant flower in the middle of my room. Remember that this is still noly a daydream but it more vivid than usual.
Then I continue to vizualize for some time until I feel like I am there! (The best feeling in the world). You just realize that the visualization is no longer a daydream, but your new reality!
This is a kind of fast transition that happens if you time REM with your awakening and DEILD attempt.
What you should look for in a WILD attempt is changes of your emotions, strange stray thoughts (subconscious or memory) and strange sensations.
You might for example suddenly think "No the bear is in the kitchen sink! Stop her Claudia!" but then you suddenly regain awareness and think "What bear and who is Caludia? o. O" I reach this state from time to time but I only transition if I manage to hold my awareness on the stray thought, also called hypnagogic imagery. This is usually naturally stable if you are in REM so if the time is right it will be automatic.

Although one also has to be in REM in order to transition (I think so anyway) so it's not always possible to transition, which is why a WBTB or a DEILD is recommended.
Another important note is that if you feel any strange sensations like see a bright light and realize that you are in your room, realize instantly that any strange experience is a sign of the dream so get up of the dreambed you probably are in! If you feel strange sensations, focus your awareness on them to increase the intensity of them and then get out of "bed"!
Good luck
Try to think that your dreams is an experience of yourself, so be aware of your thoughts and yourself in order to be aware of the dream!
Sweet dreams!
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