The main ideas in playing for a draw are to exchange as many pieces as possible, and to avoid getting into a sharp opening. This simplifies the position and reduces the tendency of either side to blunder. For each case, some openings are suitable.
If black is OK with a draw, then 1. e4 is the best. The only risk of drawing the game here is getting a sharp opening in return (a Sicilian, for example), which your opponent won't do if they are playing for a draw.
If your opponent is playing for a win, then open with 1. d4. A typical reply is a QGD, or perhaps a Slav defense. In both cases, to draw you would go for an exchange variation:
QGD: Exchange Variation
1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. cxd5
Slav Defense: Exchange Variation
1. d4 d5 2. c4 c6 3. cxd5