Beatles Acoustic Guitar Sound - How to...

This isn't much help for the bedroom producer, but the unfortunate answer is: really good microphones in some of the world's best rooms. 
 
The challenge of recording acoustic guitars is that they're, well, acoustic. As with violins and celli and hammered dulcimers, the room is half the equation. You need the difficult-to-achieve combination of a reverberant space that lacks discernable resonances. You can't get that in a small or square room, and you can't get it in a room with lots of acoustical absorption. IOW, the typical home studio.
 
What you can do is start with a microphone that does well at high frequencies. An SM-58 won't cut it. Ideally it'd be a small-diaphragm condenser, but any high-quality condenser microphone will work, preferably a multi-pattern model that will let you set it to omnidirectional mode. That eliminates the proximity effect while allowing more of the room reflections in.
 
Avoid some of the guitar's own uneven resonances by avoiding the "sound hole". The desirable sound of an acoustic guitar emanates from its top plate, not the hole. That's why most miking techniques have you pointing the mic somewhere between the neck and the hole. Experiment with how far away you can get the microphone before it starts sounding thin and nasty. The better the room, the farther you'll be able to place it. 
 
Because your room probably doesn't sound like EMI studios (and whose does?), use acoustical absorption to dampen reflections and make your room sound more neutral. It's a meat-axe solution, but the only option available for most of us. You'll just have to make up the lack of ambiance with artificial reverb.
 
Oh, and one more thought...fresh strings make a huge difference on steel-string guitars. Yeh, you'll have to constantly re-tune it but they'll be much brighter.

bitflipper

Oh, and one more thought...fresh strings make a huge difference on steel-string guitars. Yeh, you'll have to constantly re-tune it but they'll be much brighter.

I agree with the first part, but if you take care to fit and stretch them properly they'll stay right on pitch. Check the re-stringing video on YouTube by Taylor Guitars, there's more to it than you might think. Andy

Something else everyone has failed to mention is the guitar itself.
 
I have a friend who has two Martin guitars both very expensive.  One has this huge big jangly sound to it. Massive tops and lows. Records like a dream. The sound cuts through a dense mix. The other one he has has this super light delicate sound to it.  Perfect for up close micing of finger picking styles.  Beats the other one hands down.  But for big solid rhythm chords the first one I mentioned kills.
 
Every brand of acoustic is going to sound a little different.  I bet the one Beatles recorded just had the sound built right in you are talking about.
 
Remember get right back to the source and the source is the guitar itself.  New strings every time as well.  No question there.
 
You can talk all day about rooms and microphones but if what you are recording does not have the sound you are after, no amount of that stuff will help you.  Get it right at the source!  An SM58 can sound fabulous if the guitar does.  Most microphones have an amazing ability to capture very accurately whatever they are put in front of.

As well as the guitar, room and mics there's something else to consider.

Abbey Road studios used their valve REDD51 desks to record pretty much everything the Beatles did, prior to the solid-state TG12345 desks being introduced in the late 60s. EMI's engineering dept. designed and built their own desks and a lot of the other hardware used through the Beatle's period. The equipment had a very distinctive sound and "feel" and was anything but the transparent, or almost transparent, ultra-low distortion "ideal" that came along later with Neve and SSL designs. Everything went to Studer tape decks of course, with quite a lot of bouncing down sub-mixes to free off tracks for re-use.

It might be worth trying the Waves Abbey Rd REDD and TG12345, plate reverb and J37 tape deck emulations if you're after "that sound".

Thanks Michael. For the last month, I once again have been watching the old videos of the Beatles recording sessions and their live concerts. The documentary Ron Howard did about their touring "Eight Days A Week" is also highly recommended.