Look inside the shoe for a tag. Older Jordan shoes have the tag sewn into the tongue, newer sneakers have them glued to the inside and some sport a hanging tag tied to the shoe. Above the bar code on the tag you'll find a style number. Check both shoes, verifying that they both have the same style number. If they do not, they are fake. If they match, check the description of the shoe at Nike's website. Verify the description matches the corresponding style number. When the shoe description doesn't match the style number, they're fake.
Each shoe style comes with its own color scheme known as a colorway. And Nike made a finite amount of colorways for each Jordan shoe style. Each make of Jordan shoe is assigned a number based on its year of manufacture, designated by a Roman numeral. Look for the numeral on the box, the shoe or the tag inside the shoe and then look up the colorways for that number via Nike's website. If your colorway matches a listed color scheme, then they may be real. Your shoes are fake if they don't match any colorways from the shoe's production year.
Each box also has a sticker printed with the exact specifications of the shoes inside, including the Roman numeral, colorway and style number. Verify the specifications on the box match the shoe and the information found on the tag inside each of the sneakers. Look for the Nike logo and the Air Jordan logo on each box; only Roman numeral style I's and II's do not feature the jumping Jordan logo. If the shoes are reissued versions of an older make, known as retro shoes, than look for a retro card on the inside of the box and match it to the sticker, shoes and tags. Any discrepancy between any of these means the shoes are likely counterfeit.
Buy from a reputable source. If you're ordering online, do your research about the seller. Read reviews on the company or visit their contact page to look for an address. Shoes ordered online from auction sites that originate from outside the U.S. may be fakes. Complete a thorough check of the box and shoes if buying from a private seller in person. Look up the retail price of the shoe you'd like to buy on the Internet. If the in-person price is significantly lower than retail, the shoes are probably fake.