Rails curve when there are two rails placed at right angles to it. So if you form an L shape, the corner one will be curved.
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You have to make a rail track (with powered rails) put the mine cart on the rail and nudge it.
Detector rails generate redstone energy (for a redstone wire or other contraption) when a minecart is on them. You can make a simple minecart accelerator by placing rails like so: [minecart rail][detector rail][powered rail][powered rail][detector rail][minecart rail]
Get the minecart in your hand then right click it onto the rail wherever you need it.
Place it down on a rail by right clicking with it selected in your hot-bar then right click it when it's placed on the rail.
minecarts can be used on rails and for powered rails, first, put a detector rail before the powered rail, then once the minecart is detected, it powers the rail.