First question. Do you have a garbage disposer unit? If so there is highly likely a port on the side of it where the dishwasher drain line can connect. The disposer cavity provides an air gap between the actual drain and the dishwasher drain hose so there can be no possibility of a siphon back into the washer. Before attaching a drain hose to a disposer there is normally a knock out slug that must be removed inside the drain nib on the disposer.
If you have no disposer then you will have to add an air gap for the dishwasher drain line that mounts in a hole up on the back skirt of the sink. The dishwasher drain connects to the air gap and than another short hose goes to a modified sink down spout fitting before the P-trap. The air gap and alternate downspout fittings look like this:
The connection for the dishwasher water line will require the application of a Tee type fitting onto the existing faucet under your sink. The exact nature of the fittings required will depend upon the type of connections there are there now and what the dishwasher comes with. If you do not consider yourself a sometimes plumber it may be well to call in a local expert to deal with the water piping (and the drains if you so wish). Here is an example of dishwasher water line Tee connection. Note it can be a good idea to equip the branch line with a ball valve shut off. The picture shown is a Tee with the branch valve built right in.