There are so many cheap acoustic guitars you can find at brick and mortar stores and on the internet. First of all, defining what is meant by the word "cheap" is in place here. If you mean "inexpensive" cheap, that's one thing. If you're referring to "quality" or "lack of quality" cheap, that's another. Often, cheap can imply both price and quality.
If we're referring to price only, then your best bet is to find a used guitar that nobody wants anymore and try to "talk down" the price. Sometimes, a brick and mortar guitar store may have a screaming deal on a brand new acoustic guitar. If that's the case, jump on it. Other times, an online music retailer may have a huge discount as well. Just keep your eyes open in that case for good deals.
When "cheap" refers to the quality or craftsmanship of the guitar, ideally the price follows, whether up (for better quality) or down (for worse quality). Be careful here. For example, if you have a budget of $100 or less and you find a decent looking acoustic guitar online, whether it's eBay, Amazon, Musician's Friend, or some other "etailer", make sure you know what you're getting into. Usually, you get what you pay for after all is said and done. eBay is a prime example. You can often find brand new cheap acoustic guitars there or elsewhere for as little as $35. In general, these guitars are going to be for beginners, so keep that in mind when shopping around.
How do you decide if something like that is going to be a decent guitar? How can you know without first handling it before you buy it? The answer is, you can't without actually playing it first. However, you can go through the following steps to get a pretty good idea of what you're getting into.
The best remedy here is to check out the seller's feedback score, check their money back guarantee, and read the feedback comments or reviews from previous buyers. This will give you a sense of the quality of the instrument, the credibility of the seller, and unbiased feedback from real customers. If the seller gives you time to try it with a 30 day money back guarantee or something similar, and the seller has been around for a while and has a decent feedback score, and the feedback ratings or reviews from past customers check out, then you should be good to go. Make your buying decision only after doing your due diligence.
Okay, so I would check out eBay, Amazon, or Musician's Friend if you're looking to buy online. If you'd prefer to try before you buy, I'd recommend calling around and going into several pawn shops in your surrounding area. Sometimes you may find some pretty awesome deals if you're at the right place at the right time and you know how to check for quality/price. Also Craigslist or another local classifed ads site will have some used guitars up for sale. The nice thing about that is if you're close enough to the seller, you can set up an appointment with them and actually play the guitar before you buy it.
Here are a couple of cheap acoustic guitars I would recommend from Amazon in the $50 to $100 range. There's the Jasmine by Takamine S35 Acoustic Guitar, Natural which has at the time of this writing about 95 "5 star" reviews out of a total of about 139. Or there's the Guitar For Dummies Acoustic Guitar Starter Pack (Guitar, Book, Audio CD, Gig Bag) which has about 40 "4 and 5 star" reviews out of about 52 total.
If you're looking to spend $50 or less, I'd highly recommend the beginner acoustic guitar package which has already been through the test of time for over 7 years now being sold on eBay. You can watch a YouTube video for these cheap acoustic guitars here.
