Various "experts" have been claiming that the best day to buy a plane ticket is Tuesday, at least for USA legacy carriers. Compared to the others, the cheapest time for DL seems to be closer to departure; for DL tickets, you must be careful not to purchase them too early.

When you've identified a fare that looks good, you can check the fare rules to see the advanced purchase requirements, although inventory can be zeroed out just because revenue management decides to do so. I've also seen advanced purchase requirements be reduced (for the same fare and fare class) as departure approaches, for example on the BE Thanksgiving sale fares.