With beginner and elementary students, I sometimes start with a list of simple countable items that they know . For example, apple, cup, pound etc - and use the whiteboard to contrast this with uncountable words like fruit, tea, money. If they see two words side by side like apple and fruit, it's easier for them to grasp the different noun types. You can also do it randomly - get students to call out words and you put them into two lists - but it's usually better to choose words for yourself. Tricky ones like fish, paper etc can be dealt with later.
For the other question: I usually teach "Do you like" first. When the class are familiar with that, I elicit "Would you like" by miming offering a student something (or better still, bring some sweets or something!) and getting them to say my "line." You will probably get "Do you want/ do you like" etc at first - when you get (or supply) "would you like" you can put both forms on the board and give more examples to illustrate the difference. For example, "Do you like whisky/ Would you like some NOW." etc. Then they can practise "would you like" by pretending to offer tea, drinks etc to guests.
For the other question: I usually teach "Do you like" first. When the class are familiar with that, I elicit "Would you like" by miming offering a student something (or better still, bring some sweets or something!) and getting them to say my "line." You will probably get "Do you want/ do you like" etc at first - when you get (or supply) "would you like" you can put both forms on the board and give more examples to illustrate the difference. For example, "Do you like whisky/ Would you like some NOW." etc. Then they can practise "would you like" by pretending to offer tea, drinks etc to guests.