Does skipping your draw step mean you don't draw a card on the first turn of the game?

In a standard game, the player who goes first skips their draw step on the very first turn. This is established by CR 103.7a, which explicitly states that the player who takes the first turn skips the draw step of that turn. This rule exists to compensate for the inherent advantage of going first.

If a card effect also instructs that player to skip their draw step (for example, a card saying 'skip your draw step'), it does not stack or compound. Under CR 614.10, skipping is a replacement effect — but more relevantly, you simply cannot skip something you are already skipping. The step is already being skipped; a second skip instruction changes nothing.

Conversely, if the second player has an effect that makes them skip their draw step, that does apply on their first turn, since the rule about skipping the first draw only applies to the player going first. The second player normally draws on turn one.

Concrete example: Suppose Player A goes first and controls a permanent that says 'skip your draw step.' On turn one, Player A would skip their draw step due to CR 103.7a regardless of that permanent. On subsequent turns, the permanent's effect kicks in and causes them to skip those draw steps instead. The permanent has no extra impact on turn one specifically.

So the short answer is: the first player never draws on turn one due to CR 103.7a, and any additional 'skip your draw step' effect is redundant on that specific turn but relevant on future turns.