Generally different printing processes require different resolutions and amounts of image data, but there's so many variables (printing size, printing method, intended viewing distance, even subject matter of the image and colours in it!) that affect what method you'd want to go with.
For this example, printing a larger-than-standard format poster (let's say 24" x 36") you have limited options. You'd be going with "Digital" - this terms is tossed around in the commercial printing industry and encompases two primary methods - essentially laser and inkjet. The alternative to digital (no, not analogue) is 'offset' printing which uses wet printing inks, printing plates, large presses like you would imagine print a newspaper (although that's web offset, but I digress).
ANYWAYS... Digital methods at your disposal:
1.) large format Inkjet. This is very costly, the quality is largely dependent on the ability of the owner of the printer to properly calibrate it and then supply you with colour profiles (you may not think this is vital and someone like me is anal to get into colour profiling for a print for home enjoyment, but when your print is $500, you don't wan to find out 1/3 the way through printing that your pride and joy red car is coming out orangey). The upside is scale, there are extremely freakishly large printers around (think 60ft wide roles x 1000ft of paper, yup) so your size of print really is only limited by your budget.
2.) large format Laser. This is becoming more common, and the quality is great. These tend to be owned by proper press/printing shops - not your Kinkos and PrintThree type places. Don't think of your office laser printer. Think of a large format inkjet. With lasers. Badass, I know. However cost is pretty steep, they're rare to come across (large format laser is larger than 18x12, commercial photocopiers print up to that size so if a Kinkos tells you they can do large format laser for dirt cheap, they don't know what you're talking about heheh).
3.) What I'd recommend for you and what I do for my prints: Chromira! This is a setup that isn't inkjet OR laser. To oversimplify it, the printer prints on photosensitive paper (actual photo paper, the printer is in a dark room) and prints using RGB LED lights basically. So it's got no expendables, there's little to no colour variation, and because of the fact that it prints on photosensitive paper this method also allows you to get away with printing much lower resolution images than you could otherwise on laser or inkjet. For example, I've printed images at 1ft x 2ft @72dpi (which is screen resolution - anything below 233dpi is considered low resolution for printing using most methods) and it looked great. The same image on laser or inkjet, even the most expensive printers in the world, would look as jagged and blocky as printing on your home inkjet. It's not a miracle worker, but it really does mean you can print extremely large format images from a consumer level DSLR where if you went anywhere above 18x12 with the same image file on a inkjet or laser, you'd have shoddy results.
I can ramble ad nauseum re: printing, but I hope this gives you some guidance! If you want to go ahead and try printing Chromira, it's also VERY cost effective vs. laser or inkjet. There's a photographic place downtown called Toronto Image Works - they've been around yonks - and they're pretty good to deal with. If you're comfortable in photoshop setting up basic files for print (it's not hard once you do it once) you can even use their bulk printing method which is a 48" wide roll, and you pay $20 per 1ft x 4ft. So 4ft x 4ft is $80!
That covers printing methods for posters... as far as processing for print, I'm a firm believer in colour profiles. They're quite easy to set up, and really can make the difference with automotive photography between your red/blue/yellow sportscar popping off the print or laying flat and looking dull. Especially when using higher end printing systems. Sharpening is something I see a LOT of people get carried away with and ruin an image in print. The process of ripping an image for print (the commercial systems that process images and send them to the various types of printers above are called RIPs or Raster Image Processors) does inject colour and sharpness modifications based on the specific printer being used. I generally sharpen images for web a lot more than I do when printing, one of the best things to do though the first time you print with a new method is to run a test print through the setup. It's time consuming but if you really want to figure out how much to sharpen, tweak colours, and what results you'll get - gotta do a test!
"Season to taste!"
Ok, end rant. PM me if you have more questions or need help!