Unfortunately, a lot of anime available are not legitimate, licensed releases. This guide should be a good primer to help you avoid wasting your hard earned money on bootlegs. This guide is not exhaustive, however, and there are probably a couple of bootleg anime out there that could pass muster, however, I intend to help you avoid the vast majority of what's out there.
The main thing to keep in mind is that if something seems too good to be true, it probably is and is something smells fishy, it probably is.
Check #1: Price
Bootleg sets are often priced well below their licensed counterparts. You can find most of the better bootlegs for about $7/disc, however, a lot of sellers will up their cost either to take advantage of unsuspecting buyers or to disguise the fact that their item is a bootleg. When it comes to price you could do a simple search at a reputable online retailer (such as Amazon) and see what the title you are interested is selling for. It isn't uncommon to find a lower price on eBay, however, you would be very lucky to find a legitimate $80 box set for $15.
Check #2: Disc Region
Most bootlegs are "Region 0" or "Region Free" whereas the vast majority of legitimate releases in North America are Region 1. Auctions will often cite that their items are playable on any DVD player or are "Region 0". I have yet to come across a legitimate release that did not have a specific region code (Region 1 is what you're looking for if you have a DVD player purchased in North America).
Check #3: Number of Discs
Another tell-tale sign is a smaller number of discs than in the legitimate release. Most bootlegs you will find are "Perfect Collections" or some variation thereof. They are most common for releases which have already had a complete boxset release of some sort. If you do a search (wherever you searched for price should suffice) and find that the number of discs in the legitimate set total 6 but the auction you are looking at has a complete box set with only 3 discs you are very, very likely to be looking at a bootleg.
Check #4: Episodes per Discs
Most legitimate releases will have somewhere between 3 and 6 episodes per discs (although as many as 7 or 8 isn't out of the question) whereas most bootlegs will have 10 episodes plus. What the bootlegs often do is compress two discs of the original release into one so a high episode count per disc, while not definitive on its own, should raise a red flag. A 26 episode series will NOT come on 3 discs.
Check #5: "Import"
A lot of bootlegs are sold under the guise of "import editions" or "import anime". Let me tell you that unless you know for a fact you are looking at an official release from a different region (i.e. you are looking to buy an R2 release straight from Japan) there is no such thing as an import edition (at least I have yet to see one).
Check #6: "Not a Bootleg"
A lot of sellers, but not all (so don't go thinking that every seller who doesn't do this is selling bootlegs), will clearly state in their auction that the item you are bidding on is NOT a bootleg. The vast majority of the time bootleg auctions will not state this (because then they'd be outright lying to you). Again, there are a good number of legitimate auctions that do no state this but if you don't see it, it might be a good hint to run some of the other checks before bidding.
Check #7: Subtitle Language
This check will definitely not catch a lot of bootlegs but it will definitely help you spot a few of them. A lot of bootlegs have the option of displaying English or Chinese subtitles. Since legitimate R1 releases are aimed at North American audiences it would be very unlikely that the production company would include Chinese subtitles on their discs. However, a lot of bootlegs are manufactured in Asia where this would make more sense. Legitimate releases will usually have the choice if English or Japanese audio and the choice of English subtitles or no subtitles, this is by far the most common. Bootlegs will usually have the choice of English or Japanese audio and the choice of English or Chinese subtitles.
Check #9: No English Audio
Again, most R1 releases are aimed at North American audiences and English is the language of choice. When anime is licensed for distribution in North American the licensee will usually produce an English language dub to be included on the R1 release. There are many bootlegs out there for titles that have not be licensed for distribution in North America at all and these will not have an English language audio track. You will usually be limited to Japanese audio with English (and sometimes English or Chinese) subtitles. There are legitimate releases in North America which do not have an English dub but unless you know that before hand, this should be another red flag for you.
As a final note; there are some very high quality bootlegs out there. In fact, there is big business producing these things. The smaller sets (1 or 2 discs) will come in standard DVD cases with nice slip cover art work. The larger sets often come in nice, gatefold boxes professionally produced with art work and everything. The DVDs are even pressed and not just DVD-Rs (another trick that bootleg sellers often use to confuse people is by saying that they aren't selling DVD-Rs, therefore, they must be legit, don't fall for this!!) with professional artwork on the discs (not just stickers).
Just use your common sense and run the above checks if you're not sure. If none of the above tests make you think you're looking at a bootleg there is a very good chance you're not, however, if you still have any doubts, move on to another auction where you feel more comfortable about the legitimacy of the item.