Putting is an art form and reading the green correctly is difficult at the best of times, so avoid increasing the difficulty for a fellow player or risking their wrath.
Be aware where their ball or marker is at all times and don't step or walk on that line to the hole.
Even if you're just tapping your ball into the cup, stand astride your playing partner's line or an extension of it - this is a courtesy every golfer will appreciate.
Another bit of advice on the greens when your playing partner is putting, make sure you are out of their sight line. So try not to stand behind them or behind their view of the hole.