Can you tap lands for mana before casting a spell to make sure you have enough?

When you cast a spell, you don't need to have mana floating before you announce it. The rules build mana payment directly into the casting process. After you announce the spell and make all choices (targets, modes, etc.), you then activate mana abilities and pay costs simultaneously (CR 601.2h).

Mana abilities are special: they can be activated any time you need mana, they don't use the stack, and they resolve immediately (CR 605.3a). This means tapping a land for mana is nearly instant and is always available during the payment step of casting.

You can tap as many lands and activate as many mana abilities as you need during that payment window — you just have to pay the full cost once you're done. You cannot, however, partially pay, then pass priority to draw cards or take other actions before finishing payment.

Example: You want to cast Lightning Bolt (cost: 1R). You announce the spell, choose a target, then tap a Mountain for R and tap a basic Plains for W — wait, that won't work. You must produce mana that satisfies the cost (R or colorless). Tap a Mountain for R, and that fully pays the cost. Payment complete, the spell is cast.

So in short: yes, tapping lands for mana is done as part of casting a spell during the payment step (CR 601.2h), not before — but the effect is exactly what you'd expect. You choose to tap your lands right when you cast.