In what position is it to be recited?
One should say it while still sitting or lying on his bed.[1] [One who sits up on his bed is to do so without placing his feet on the ground.[2] One is to place one hand against the other, and lower his head upon reciting Modeh Ani.[3]]
[1] Basra 1:6
The reason not to stand: The reason for why one should not stand is because Modeh Ani is to be said immediately upon awakening and one should not suddenly stand up on his feet immediately upon awakening. [Basra and Kama 1:6] The reason for this is because one who does so is closer to death than life. [Kama ibid]
[2] It is our custom not to place our feet on the ground until after washing hands, as will be explained in Chapter 4 Halacha 3 Q&A
[3] Sefer Haminhagim p. 3 [English Edition] based on Sichas Chag Hashevuos 2nd day 1949 chapter 13 printed in Sefer Hamamarim 5750 p. 244; See Hiskashrus 623 p. 16
Background:
The Rebbe Rayatz stated the following during a gathering on the 2nd day of Shavuos 1949: When they educated me to say Modeh Ani they told me to place one hand over the other and to nod my head downwards while saying it. When I was a bit older, although still a child, I asked my father for the reason behind this custom. He answered me: In truth you must fulfill without asking why, although since I told you to ask me all your questions [I will thereby give you an explanation]. My father then called into his study the beadle Yosef Mordechai which was 80 years old at the time. He asked him how he says Modeh Ani and he answered that he proximate his two hands together and lowers his head. He then asked him why he does so and he answered “I don’t know but that is how I was taught to do it since I was a child. My father than replied: You see he does it because his father taught him to do it that way and so on and so forth all the way back to Moshe Rabbeinu and Avraham Avinu which was the first Jew. A Jew must comply by his tradition without asking why he must do so. [ibid] Rabbi Leibel Groner stated that when he compiled Sefer Haminhagim he was in doubt whether to enter this custom into the Sefer and the Rebbe answered him to do so as it is a directive that is pertinent to the public. [Hiskashrus 623 p. 16]