You unlock weapon swapping at level 15. When you reach level 15, your inventory screen will change to show "Main hand weapon / offhand weapon" and "backup weapon / offhand backup weapon". You need to have both the main and backup weapon slots equipped with weapons for weapon swapping to function.

Once you have equipped both weapons, the left directional pad (on PS4) will quickswap between the two. Each weapon set comes with it's own ability bar, so you'll have to slot your skills on the ability bar for each weapon seperately.