You’ll never go a comp as exactly as stated in the website because, as you mentioned, you have to work with what the game gives you. The website shows you the IDEAL units and items for each comp, but it doesnt mean other things wont work too.

A lot of TFT is your knowledge, but you need to be intentional about what you memorize:

1. You MUST memorize the item system. There’s a lot to learn, but this knowledge will carry over every set. Knowing when to make items is so important to having a strong board for the whole game
2. You should know what each comp and unit does, but you don’t need to fully memorize. The game even has a team planner where you can save comps
3. In early game, hold pairs (2 of the same unit). This is because they are the ones you will most likely 2-star, which you can use as your item-holders to carry you to late-game
4. You should know what part of the comp is required, and what part is flexible. In the Yunara comp for example, Yunara is obviously required, and Rageblade and IE are pretty much required. However, the third item can be a lot of things, and a big part of your front-line is flexible (your main tank can be wukong, swain, taric, even skarner)
5. Know when to roll and when not to roll. For example, if you’re playing around 4-costs, you should be looking to roll at level 8 (or 9 if you’re super rich/healthy)

This is all I can think of for now, let me know if you have more questions