What does the Guns button do?

This takes you to the weapons offer screen. Here, you will be shown various weapons that are on offer.

You can find more information on the shown weapon by tapping the "i" button on the left.

You can purchase the shown weapon by tapping the Gold button on the right. If this button states "SOLD OUT", this means that the offer is no longer available, or you already own the weapon.

You can also tap the "NEXT OFFER" button on the right to scroll through the different weapon offers.

You can choose which mode to purchase guns for by tapping the buttons just above the weapons at the bottom. Standard indicates Campaign and PvP-focused guns, Arena indicates weapons that are designed to be used in Arena missions, and Zombie/Robot indicates Zombie/Robot Event guns.
Finally, tapping any of the weapon types at the bottom will take you to the Weapon screen for the type that you selected.

As you upgrade your weapons from here, you may see the text "Overload" appear above the payment options. This appears once you have upgraded the weapon part to its limit for Campaign mode. Any further upgrades will only apply to PvP for standard weapons (overloading arena and event weapons work like normal upgrades except it focuses on one stat).