I will be replacing my dishwasher and I am curious what is the current code for the wiring of the dishwasher.
Assuming you're in the US (though I can't imagine it being much different elsewhere, but do check!) ...
Be sure to check the label, but most dishwashers run perfectly happy on a 15A circuit. If a dedicated circuit to the dishwasher isn't possible, you can come out of a general receptacle circuit that isn't otherwise utilized in the kitchen, depending on the rating of the dishwasher. What you want to avoid is a mixer and toaster and dishwasher using the same circuit at once. You may have to do some investigating. Go for the dedicated circuit if that's possible.
If the dishwasher has a cord and cap, you should have an appliance receptacle installed where it can be reached. An appliance receptacle is an outlet with only one place to plug something in. Since your dishwasher can not be on a GFCI circuit, this ensures that someone won't try to plug something else into the non-GFCI protected outlet while near ground potential (within six feet of anything wet, e.g the sink). Even if the plug is somewhat hidden or inaccessible, you want to be sure nothing else uses it. Be sure the receptacle is rated properly, they come in 15 and 20 amp varieties.
If the dishwasher has a place to just terminate a cable, purchase the appropriate connector for the type of cable you're using (likely ROMEX (non-metallic + bonded)) to go into the 1/2" opening, secure the connector properly and make the connections using wire nuts.
Be kind to your future self, or anyone else that has to pull the dishwasher out in the future to service it by leaving enough cable to be able to pull it out and off to the side. Make sure the cable is secured properly wherever it is fed, and protected anywhere that it may be exposed on its path to the dishwasher.
If uncertain or uneasy - you probably want to call an electrician.