How does one "get rekt"?

Solution 1:

Get rekt comes from Get wrecked. See here.

Telling someone to "get wrecked" (in the context of a game) can be similar to telling someone to "go kill yourself." Implicit in the imperative is that the person it's directed at is so bad or that the commentator hates them so much that they ought to just go kill or wreck themselves.

Of course, as is common with slang, it is often used with heavy amounts of irony or non-seriousness.

It can also be used as a standard imperative instructing the interlocutor to get wrecked or destroyed. The slight irony here is that you give the imperative after the wrecking has already happened.

Solution 2:

Explained well by Urban Dictionary

Get rekt m8

Mostly used after getting good kill or shot, in mostly FPS (1st person shooter)  Rekt is a misspelled version of the word "Wrecked". M8 is meant to be M + Eight = Mate. So it's get wrecked mate

360 degrees headshot with a sniper rifle without even aiming in some random Call of Duty game (also 360 noscope).

Me: Ha get rekt m8.

Victim: bwahahahaa, im such a noob

If you want to see the Xfactor judges get rekt have a look at https://www.youtube.com/watch?v=f4EwKrTgtLQ

EDIT: Get wrecked per se, means get injured or beat up. See Urban Dictionary again.

Solution 3:

I think we can trust the entry in knowyourmeme.com on this one...

“Rekt”, also known as #rekt, is an Internet slang term which is shorthand for “wrecked,” which is often used in online gaming to indicate that someone has been defeated or embarassed, in a similar vein to the term “pwned”.
Origin
On June 6th, 2011, Urban Dictionary user PossiblyCouldOKIWill submitted an entry for the term “rekt,” defining it as text message slang for the term “wrecked”:
“Text for “wrecked”, as sooo drunk you’ve forgotten your name but can just about type a text to your mate whose missed called you"
Spread
On October 13th, 2012, World of Warcraft Forums member Balrogboogie started a thread titled “Get Rekt Ally Scrublords.” On October 13th, 2013, Tale Worlds Forums4 member Unicorn submitted a thread about the “REKT” North American Dueling tournament for the role-playing game Mount and Blade. On October 31st, Twitter user @SSoHPKC tweeted his idea for a Halloween prank accompanied by the phrase “Get reKt.” Within the following four months, the tweet gathered more than 490 favorites and 440 retweets.

Note that wrecked = (very) drunk is primarily a British usage, so most likely the vast majority of people using rekt in recent years aren't familiar with that sense. They simply see it as a "cute" way of writing a word that means destroyed (figuratively, totally defeated in online games, etc.).

Solution 4:

In regards to the other answers, they have given (from what I have read) a non-gamer response.

Their response's are correct, but in, I believe the way you're asking, the term "get rekt" would mean the person saying it just "killed" or "beat" etc.. in whatever it is/was they are doing.

Basically, its a term for saying you just lost.