How I Met Your Mother - Ted´s Wife

 
 
"How I Met Your Mother" is a show about Ted (Josh Radnor), and how he fell in love. It all starts when Ted's best friend Marshall (Jason Segel) drops the bombshell that he's going to propose to his long-time girlfriend Lily (Alyson Hannigan), kindergarten teacher.
At that moment, Ted realizes that he had better get a move on if het too hopes to find true love. Helping him in his quest is Barney (Neil Patrick Harris), a friend with endless, sometimes outragous opinions, a penchant, and a full-proof way to meet women. When Ted meets Robin (Cobie Smulders), he's sure it's love at first sight, but destiny may have something else in store.
The Tv-Show is basicly about the life of Ted from college until he gets married. Ted is the narrator of the story and tells it to his kids in in form of a retrospective.

 
What we know about Ted´s Wife is that...

...own´s a yellow umbrella and was on the same St. Patrick´s Day-Party as Ted and Barney, where i think we see her the first time.
“Bump Girl” is the nickname fans have given to the character played by Nicole Muirbrook Wagner in the third season episode “No Tomorrow.” Her entire scene amounts to Ted accidentally bumping into her while walking through a nightclub, Ted briefly apologizing and her graciously dismissing him. This was discussed immediately after the episode when fans, myself among them, noticed this girl.
Because Ted earlier notes that the Mother was in the nightclub that night but that he didn’t meet her, some casual fans have jumped on the theory that since the scene is pointless otherwise, Bump Girl must be the mother.The trope that “Bump Girl” is riffing on is that of The Conservation of Information, also known as “Chekhov’s Gun“–you don’t show something if it’s not important.

 
...she share´s an apartment with Cindy, who is Ted´s girlfriend for a while and dosen´t like her flatmate, because all the guys prefer her

...she sat in the lecture hall, when Ted was in the wrong classroom (so she studies economy)

...she met Ted on Barneys wedding
 
So Ted´s Wife is Barney´s half-sister, because she went to college and Ted saw her the first time, when he was in the wrong classroom.

Since Barney doesn't know who

his dad is yet, he will later find him, who will have a daughter.

And as Dash said in the comments, when Barney's Brother, James Stinson adopted a baby, this was how Barney became uncle Barney. So Barney is Uncle to his brother James's kid, and will become Uncle again when his sister has a child with Ted.

Update:

 

In the episode Legendaddy, Barney meets his real father and it is revealed that he has a daughter called Karly who is in collage, and that his father lives near by. It has been

mentioned that the mother was in an economics class that Ted mistakenly lectured at. Also, because we didn't meet her when Barney was at there house, it can mean that she lives
elsewhere - I.e Cindie's house. As per meeting the mother at the wedding, this will be Barney's wedding, possibly with Nora (in which Barney's sister is introduced into the show) and that's how Ted and the future mother meets)

You can watch How I Met Your Mother for free on:
http://www.cucirca.com/2009/06/05/watch-how-i-met-your-mother-online/