Showing a Set is countable

Quick question about setting up this problem:

Determine if the set is countable or uncountable. If countable, exhibit a one-to-one correspondence between the set of natural numbers and the set.

1) integers not divisible by 3

2) real numbers with decimal representations consisting of all 1s

I understand intuitively what it means to be countable or uncountable, but what i dont know how to do is SHOW this. Frustratingly enough, our teacher doesnt instruct us on the methods to solve problems, he just shows such things to be true while not explaining how he gets there...

Any help would be appreciated!