In the Movie
In The Muppets, Tex Richman is an oil tycoon who is the owner of Richman Oil. He plots to buy the Muppet Studios, claiming that he wants to turn it into a Muppet museum, but the truth is that he wants to destroy it and drill for oil that is underneath. He claims that he used to love the Muppets, but in reality (revealed partially in the operatic part of "Let's Talk About Me" which was never used in the film), he has never laughed and has always hated the Muppets ever since he was 10. He shows no sympathy for the Muppets and degrades them to their faces. Ironically, he has four Muppets as his "Evil Henchmen": Bobo the Bear, Uncle Deadly and Statler and Waldorf.
The deal made was that if the Muppets could not raise $10,000,000, they would lose both the studio and the Muppet name, stating that he would then give it to The Moopets.
He tries to sabotage the Muppet Telethon using several methods. First, he crashes the Muppets' car into a pole, thereby cutting off the power. He then tries to cut an antenna, but is then foiled by a reformed Uncle Deadly.
After the Muppet Telethon is over (and revealed to be a failure), he tells the "Artists Formely Known as The Muppets" to leave his Property. The Muppets leave, sad-hearted over the fact that Tex has won.
During the finale with "Life's a Happy Song", he appears begrudged that the Muppets still have a huge crowd of fans cheering them on, hinted by the way he says, "Will you please stop singing? You've already sung this song." He isn't seen again until the credits.
In the Credits
In the credits of the movie, Tex is hit in the head by Gonzo's bowling ball that was supposed to be used for his "Head Bowling" stunt in the Telethon. This injury caused Tex to actually laugh for the first time (not just maniacally, as he did several times earlier in the movie). He also had a change of heart, making the decision to give the Muppets back their studio and their name. According to a press release, this was due to a "change of heart and had nothing to do with the head injury". The Moopets were not happy and they demanded Richman to pay them back as apart of their "deal".
Not much is known about Tex Richman's early life or why he is in the oil business. During his song "Let's Talk About Me", he reveals a tiny bit about his past.
During the spontaneous musical number (in the bridge that was deleted from the theatrical release), he recalls a heartbreaking story about his 10th birthday party. He thought it was going to be a great day. But the Muppets were putting on a show (it is unclear by what he meant by "...the Muppets were there to put on a show...", they were either physically there or on TV). The other guests were laughing, but Tex himself did not know how to. Then (according to him), the guests turned around and laughed at him. Since then, he has hated the Muppets and does not understand why people find them funny.