The online guides have left me unsatisfied with the faithfulness to the source material. Therefore, I would like to present, arguably, the most accurate guide to making the in-game drinks.
The most important sources are: item descriptions, item images, and character dialogue. The animations and models often seem to not correspond with what the characters or the descriptions are actually saying, so they should be dismissed.
The David Martinez (easy)
[1] – the item description calls for NiCola. Since the color of the drink is blue, the drink is specifically the limited edition NiCola Blue. Use any blue fizzy drink for this. I suggest the berry Fanta; it should evoke the taste of cough syrup, but blue.
[2] – evident from the image. I have been squinting at the image for quite long, and it appears that a lemon peel is the source of the yellow hue. The glow is creative license.
[3] – evident from the image.
The Jackie Welles (medium)
[4] – at Lizzie's Bar during "The Corpo-Rat," Jackie orders "double tequila with grenadine and lime." Since the image has a clear reddish hue, "a splash of love" must stand for an actual red-colored ingredient.
[5] – evident from the image.
[*} – there appears to be some kind of sunken straw or garnish on the image. Might be artist's error. I can't quite make it out, but moscow mules are often drank with straws, so you are welcome to add one in.
The Johnny Silverhand (hard)
[6] – mixing tequila, agave syrup, and bitters is how you make it old-fashioned.
[7] – in "Chippin' In" Johnny says "And sprinkle in some chili." Having chili on the edge of a glass looks really nice, but if you want to be accurate, it needs to be sprinkled.
[*] – you may have to use darker beer to get the right color.
Sorry if I messed up any of the drink terminology or proper order of assembly. Let me know if you have any tips. Cheers!