In survival, to break a minecart, all you have to do is right click a couple times on it. Do not hold the right mouse button down because it will not work.
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I think you mean "How do you get in a minecart in minecraft?". First, you place the minecart, preferably on minecart tracks, then just right click on it. If you are not on a powered rail, You need to push it first.
let it sit then push it in the minecart.
Get the minecart in your hand then right click it onto the rail wherever you need it.
You could push the minecart, although you wont go that far. You can also try powered rails to push your minecart forward.
Right click the minecart.