Is there an explication of how Geralt and Yen first met or the circumstances in which they met? Since I cannot find the books in my country and E-book is not an option for my eyes, I ask here. Only in the games or the books, (I played the games 2 and 3), and no fan-fiction please.
They meet in the story called "The Last Wish". Spoilers!
Basically, Geralt and Dandelion were fishing (unsuccessfully) and stumbled upon an amphora of sorts. The amphora had a seal, and Dandelion, being an idiot (as usual), decided to break the seal hoping that there is a genie there that will grant him three wishes. He was even able to voice 2 wishes - make some girl agree to have sex with him and kill his rival troubadour Waldo Marx - but genie was not so cooperative and almost choked him to death. Geralt banished the genie, but since Dandelion was injured (his throat, a troubadours main tool), Geralt took him to nearest town, which supposedly had a sorceress who could help.
The sorceress Yennefer agreed to help, but it turned out that she wanted to tame the genie to use its powers. To do that, she needs the genie to grant all 3 wishes to Dandelion (he already voiced 2).
Major plot twist here comes when Yen realises that it is not Dandelion who voiced the wishes - it's Geralt, because he grabbed the seal. First time he grabbed the seal and used and "ancient exorcism he learned from a priestess" (which actually translates as "go away and plough yourself" - Geralt didn't know the translation, obviously), and the second time he asked the guard captain in the prison to "explode". Then the guard exploded.
Eventually, Yen figures this and tames Geralt to voice his last wish - she asks him if he wants to be normal, etc.
Ultimately, the "camera" leaves Geralt and Yen when genie, being angry as hell, almost reaches Yen and Geralt finally voices his last wish.
There is a lot of speculation regarding the nature of Geralt's last wish, but Sapkowski intended to leave it to the imagination of the reader.
There is a side quest in The Witcher 3: Wild Hunt, called The Last Wish, after Kaer Trolde storyline (basically, Yen asks you for a favor, and it's not what you think) that expands this story:
Yen once again wants to bind a genie, but this time in order to make him cancel Geralt's last wish. If you do help her and cancel the wish, you only can chose an option where Geralt says that nothing has really changed between them, i. e. their love (if you can call it that way) is real and not magically-induced. Yaay, happy end!
Yes it is explained in the story "The last wish" (published in the book with the same title). Short version (you can find full version on Wikipedia). Obvious spoilers below
Geralt and Dandelion find an ancient amphora - bard believing that this is a wish granting djinn rubs it while the Witcher tries to stop him. In the end they accidentally unseal the jar, but the mysterious red mist chokes Dandelion instead of trying to fulfill his wishes but Geralt manages to send the monster away by speaking quickly "an exorcism" * he heard from some priest.
After arriving in nearby town Geralt finds that an enchantress is staying in the inn - after hearing his story Yennefer decides to help Dandelion, but as a form of payment she enchants Geralt and sends on a rampage through the city, when he punishes everyone who ever wronged her.
After awaking in the jail and being taunted by guard, Geralt mumbles "I wish you'd burst"... and guard indeed explodes, to everyone's huge surprise.
After being summoned to the mayor to explain himself, huge thunderstorm breaks loose outside - its the Yennefer trying (and failing) to capture the djinn. Realising that all this time djinn was fulfilling his wishes (Geralt was holding the seal blocking the amphora), Geralt says his third wish (never explained) saving the enchantress.
He literally told the genie "Go and f*ck yourself".... "Your wish is my command, master..."