Can one move their garbage bin from the street curb to their house on shabbos in order to use it? Will it make a difference if the bin is empty? Or if it’s on Yom tov?
It is permitted to move the garbage bin if it is empty, but not if it is full.
The reason for this is that when full, the bin is a basis for the garbage, and therefore cannot be moved; but when empty, it is permitted to move it.
There is no difference between Shabbos and Yom Tov for this matter, except that on Shabbos this assumes of course that there is an eruv in the relevant area.
An empty garbage bin is not muktzeh.
The reason for this is that although they are muktzeh when Shabbos comes in (because they are a basis for the garbage), one knows that they will be emptied out on Shabbos, and therefore the principle of migu de’iskazai does not apply (see Beitzah 26b). This is not even a case of dechiya beyadayim, because the whole purpose of taking out the garbage cans is not to ‘push them away’ but rather to enable one to use them later after they are emptied. Therefore, the idea of gamro bidei adam will certainly apply.
For the question of whether garbage cans in general are muktzeh on Shabbos, see here.