You need to put some apples in the blender. It helps if you wash and quarter them (weaker blenders need the quarters cut in half) but you don't need to core them. Add a little water (how much you need again depends on your blender motor) and blend until... well, until blended.)
Now you need "cheesecloth." Ideally you should use butter muslin, which is the cloth that is actually used to make cheese. The cheesecloth you can get in grocery stores is useless for separating liquids from solids. Butter muslin can be ordered from cheesemaking suppliers; you can wash and reuse it. If you don't have butter muslin, however, a non-terry towel will do.
WASH YOUR HANDS.
Dump the apple goo into your cloth, over a pot. Gather the ends of the cloth and starting from the top, twist the cloth up. Add twist, moving downwards, to put pressure on the apple goo and squeeze the juice out. This doesn't take too long; a minute or two will give you a pot full of juice and a hard little puck of apple solids.
If you like fresh, tart juice you can drink this or refrigerate and use within a couple days. If you want to keep it a little longer, or if you like your juice sweeter and less crisp tasting, bring it to a boil on the stove first.
There has to be something good that you can do with those apple solids, but being insufficiently imaginative I usually just compost them.