Did Spielberg have any involvement in filming Star Wars?

Spielberg was busy directing Close Encounters of the Third Kind at the time. While they discussed their projects,

Prior to [Star Wars's] release, George Lucas showed an early cut of the film to a group of his film director friends. Most, including Lucas himself, felt the film would be a flop; Brian De Palma reportedly called it the "worst movie ever." The only dissenter was Steven Spielberg, who correctly predicted the film would make millions of dollars.

Spielberg did not help him direct. He did recommend John Williams to compose the score,

George Lucas planned to score the film with existing classical music like Stanley Kubrick had done on 2001: A Space Odyssey (1968), before Steven Spielberg introduced him to composer John Williams. Lucas and Williams agreed on a classical 19th-century Romantic music style with liberal use of leitmotif for the score. Since the movie would show worlds never seen before, the music had to serve as an "emotional anchor" for the audience to relate.

and also made some money on a bet.

After visiting the set of Close Encounters of the Third Kind (1977), George Lucas was sure Close Encounters would outperform the yet-to-be-released Star Wars at the box office. Steven Spielberg disagreed, and felt Lucas's Star Wars would be the bigger hit. Lucas proposed they trade 2.5% of the profit on each other's films; Spielberg took the trade, and still receives 2.5% of the profits from Star Wars.

Steven Spielberg is listed as a guest director in Episode III: Revenge of the Sith. However, he has ruled out directing an entire SW movie, as stated here:

"I've asked [Lucas]. He won't let me do one," he said. "I wanted to do one 15 years ago, and he didn't want me to do it. I understand why - Star Wars is George's baby. It's his cottage industry and it's his fingerprints. He knows I've got Jurassic Park and Raiders. But George has Star Wars and I don't think he feels inclined to share any of it with me."

Spielberg was one of several directors who joined the studio executives for a screening of the original film:

In February 1977, Lucas screened an early cut of the film for Fox executives, several director friends, along with Roy Thomas and Howard Chaykin of Marvel Comics who were preparing a Star Wars comic book. The cut had a different crawl from the finished version and used Prowse's voice for Darth Vader. It also lacked most special effects; hand-drawn arrows took the place of blaster beams, and when the Millennium Falcon fought TIE fighters, the film cut to footage of World War II dogfights. The reactions of the directors present, such as Brian De Palma, John Milius, and Steven Spielberg, disappointed Lucas. Spielberg, who claimed to have been the only person in the audience to have enjoyed the film, believed that the lack of enthusiasm was due to the absence of finished special effects.

Despite the reaction of the other directors, the studio executives loved the film, and committed additional money to finish the film.