So, your reading this because you need a Pokémon without the Premier Ribbon automatically applied by the Pokécheck server (in most cases). Primary reason being for use in Random Matchup or more official Pokémon tournaments such as VGC, GBU, Spring Friendly, or some unofficial tournaments on sites such as Smogon, Serebii, or Marriland. 

A few functions of Pokécheck do not apply the Premier Ribbon. They are "Pokeshift" (Queue for transfer to Generation 5) and "Download .pkm file". If your desired Pokémon is Generation 4 format and you want it on your Generation 5 game, simply hit the "Queue for transfer to Generation 5" button and download the Pokémon on a Generation 5 game. No ribbon, no hassle, no problem. If you need to use a Gen 5 Pokémon on a Gen 5 game, which is probably the entire reason your reading this, your going to have to use the .pkm file. Same also applies to using a Gen 4 Pokémon on a Gen 4 game. If you used Pokeshift, your done.
The "Clone on GTS" option also has no restrictions, aside from a yellow addition to the clone status of your Pokémon. However, Mandrew's guide covers that nicely http://pastebin.com/hSZV988k

**Using the .pkm file**

The first step finding a legitimate, or at worst legal Pokémon to use. I leave that to Pokécheck's top-notch Legality Analysis and your common sense. When in doubt, you can use a nice list of known RNGers like this one http://thegamingforum.org/forum/f11/the-official-pok%E9check-thread-282/#post2542 . After that, simply hit the "download .pkm file" button found at the bottom of a Pokémon's page with all the other shiny world-ending buttons. I'm hoping you know how to save a file. Don't run it or anything, just save it somewhere you can find it, like your desktop.   

Second step is just as mind-numbingly simple. Simply upload the .pkm file to http://pokegts.us/5thGen_Upload.aspx , change your DNS setting to the DNS listed at the top the same way you would for Pokécheck. And then connect to the ingame GTS -WITH A FULL PARTY- and your Pokémon will download straight to the first open spot in your PC. 
Use the Gen 4 tab for Gen 4 games obviously, and do make sure the .pkm you downloaded was in the proper format. Or it'll come out... well, horrifically. 

Yep, that simple. Enjoy the Pokémon, slay many foes, etc etc. Now back get back to Pokécheck and enjoy the site http://www.pokecheck.org/ .