LittleBobbyTales is correct about the tournament rules.
Beyond what he has said, (in tournament rules) if the first player for one reason or another accidentally does not make their first play across the center tile and then hits their clock (signaling the end of their turn), the second player has the option to point this out and make the first player remove the play and play again or accept the play. If the play stands, the first play is not doubled, but it is scored according to whatever premium squares that it covers. The second player may then play across the center star, earning a double word score. In this sense, the center star is exactly like a
Double Word Score square. This does actually happen occasionally in tournaments, sometimes leading to a rare "triple-double," where the second player plays an 8 letter word from the
Triple Word Score on the edge of the board to the center star, through the first word, garnering a six times word score.
It should also be pointed out that it is often good Scrabble strategy to play the first word off-centered from the center star (i.e. contrary to the second bullet point). Tournament Scrabble players specifically study 5-letter words with high point tiles at the beginning or the end in order to play them with the high point tile on the
Double Letter Score five squares away from the center star. Also, it is good technique to avoid putting vowels next to the
Double Letter Score squares in the rows above and below the center star row (or to the left and right, if the word is played vertically). This avoids the danger of having the second player make a parallel play with a high point letter on the
Double Letter Score, garnering four times the value of that letter.
Finally, a number of tournament players play their first word vertically, but the majority don't. It makes no difference, particularly in a casual game, since the board is symmetric, but some tournament players do it to throw their opponent off of their rhythm.