The quality and resolution of the original image will affect how well the image works as a poster. For full photographic resolution, you need 300 pixels per inch (ppi). For an image 3000 x 2000 pixels (~6MP), that gives you 10 x 6.7 inches. You can stretch this to 200ppi (15x10") with no noticeable loss of resolution. However, since posters are meant to be seen from a few feet away, you can sacrifice some ultimate resolution without looking too bad. Images printed at 75ppi will not look photo-sharp viewed close up, but look fine hanging on the wall, if the original image is good quality. That would give you a 40 x 27" poster. Be aware that if the original image isn't sharp and clear, it can look pretty shabby blown up, as any noise or blur will become very obvious.
The best way to enlarge digital pictures for poster printing is to rescale them to 300ppi at the intended print size. Photoshop, Gimp, Irfanview, and other image editors can do this. Specify that you want to resample, and choose smoothing if it's offered. The place that prints the posters may be able to do this for you, as well.
Just to see what it would look like, I recently printed a portion of a photo at 25 pixels per inch, re-sampled and smoothed. It looked more like a water color than a photograph, and there was a little stair-stepping on some straight lines, but for a photo where color and composition were more important than detail, it just might work.