This used to be really difficult - when car radios were AM only. Getting the hum and noise out was a complex task to say the least. If you are after HD-AM, be prepared for a lot of time experimenting with the power supply and grounding to get it right. I eventually made an old Delco into a really good AM DX radio. They were very nice for the task because the IF frequency of 262 kHz allowed better selectivity than usual.
Fast forward 40 years, and all the comments above still apply. I will add that the average car radio probably runs a bit better off 14V than 12V because the alternator in most cars runs at 13.5 to 14.5. Also, the cell voltage of lead acid batteries is slightly above 2V, put six of them in series and you get somewhere between 12.4 and 12.8 out of a charged car battery.
A lot of newer car radios have a bridged speaker output - one side is NOT grounded, so if you ground the speakers you will burn out the radio. At the very least - if you must ground the speakers, make all speaker connections through 2200uF or greater capacitors.
When I did the car radio, made a wooden case and cut out a rectangular opening for the dial, two holes for the shafts. Most car radios today require just a single rectangular opening. Making a suitable case requires wood working skills, room for the radio and room for the power supply. Beware of some universal supplies sold in places like Frys - they are small with plenty of current - but they are switching supplies which will make the noise problem worse. I've made a fair number of linear supplies using a transformer, diodes, big caps, and LM317's which can be programmed to 14V easily. I'd suggest 162 Ohms and 1.69k Ohms for the output voltage setting resistors - about as close to exactly 14 as you will get without a pot.
It is getting harder and harder to find aftermarket antennas, but they are still available at most auto parts houses. Definitely get the expandable whip kind - with FM the 31 inch length would seem to be tuned, but I get much more sensitivity with the big 60 inch expandable whips. Definitely better for AM as well.
You can find piles of bookshelf speakers at most electronics surplus houses - they last longbi after the pathetic receivers they were attached to have long since quit. Even if the speaker cones are rotted out, replacements are easy to find, buy the bookshelf speaker set anyway just for the nice finished cabinet.
HD FM is a bit anemic as a transmission method, you may have to rig an outdoor antenna to do the job. You will need an FM only model, with as many elements as you can get, convert it to 75 ohms with a transformer on the antenna, and wire 75 Ohm coax directly into the car radio. There is a bit of an impedance mismatch, but the extremely good gain of an outdoor antenna over a whip will overcome that many times over. You may even have to attenuate a bit, because the car radio is designed for a whip - more gain from the antenna system may cause overload. But the outdoor antenna is there as much as anything for directionality.
Unfortunately, hooking the car radio to an outdoor antenna will not help AM. You may need a two way switch for antennas.
As table top HD radios get rare, this question may come up again! It seems that car radios are the only HD radios selling - and being sold- these days.