Luke Skywalker^wp was trained by Master Yoda, Master Kenobi, and picked up many things from his duels with his father, Darth Vader. Although difficult to attribute his lightsaber style, it is theorized that he specialized in Form V: Shien / Djem So after his father.^source?

Luke Skywalker is not the creator of this hilt. However, the design is different from Anakin Skywalker's original in Revenge of the Sith and thus is attributed to Luke here. Rebel Scum has a great article on the differences. Frank Bruton was the property master for A New Hope and had this designed off of a 3cell graflex flash tube.

This hilt was given to Luke by Obi-wan Kenobi the first time they meet on Tatooine. Luke would modify this version slightly as he progresses with his training.

This hilt it attributed to Luke even though the base was made by Anakin Skywalker because he modified it to make it his own. Rebel Scum has a great article on the differences between this one and the one from ANH. Frank Bruton was the property master for A New Hope and had this designed off of a 3cell graflex flash tube.

Luke modifies the original hilt during his training as a jedi.
Luke will lose this hilt during his duel with Darth Vader in cloud city when his hand is cut off.1)
Joruus C'baoth will recover this lightsaber along with Luke's hand to give to a clone of Luke Skywalker. After Luke defeats the clone he gives the hilt to Mara Jade.2)

So far there have been three versions discovered of this hilt. The first hilt, v1, is only used for the close up shots of Darth Vaders hand as he's examining Luke's saber after being captured on Endor and the rest of the shots use v2. V2 was actually a leftover Obi-wan Stunt from ANH. The V3 hilt was seen at a special exhibit/screening for employees only and is not known where it was used in the actual film.

This is the first Hilt that Luke actually makes on his own using instructions from Obi-wan's original designs. He constructs this lightsaber on Tatooine before heading out to rescue Han and Leia.3)

Additional hilt designs can be seen for Luke Skywalker in the expanded universe section.