After the resolution of the triggered ability, Gwenom lets you look at the top card of your library whenever you want (with one restriction—see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand. Once the effect has ended in your cleanup step, however, you may not look at the top card anymore.

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

If the top card of your library changes while you're casting a spell, playing a land, activating an ability, or taking a special action, you can't look at the new top card until you finish doing so. This means that if you cast the top card of your library, you can't look at the next one until you're done paying for that spell.

If you cast a spell for another cost "rather than pay its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as a kicker cost. If the card has any mandatory additional costs, those must be paid to cast the card.

You can play a land card from the top of your library only if you have available land plays remaining.

You must follow all normal timing rules when playing a land or casting a spell this way.