Flow chart for DS4 controller interface?

[Niwashi]

Up/Down - cycle through party members
Left/Right - target things in front of you according to current targeting filter (see below)
L1+Up/Down - cycle through enemy list
L1+Left/Right - cycle through alliance list
L1+X/O/Triangle/Square - select targeting filter (see below)

All of these start as a soft target. To make them a hard target, select them as above, then press X to confirm the choice. If you have something soft-targeted when you use a skill, it will perform that one skill on the soft target, but then switch your target back to whatever is hard targeted. (It's useful to use that way for a healer who wants to attack an enemy while keeping the tank targeted for healing, or a DPS who wants to send a support buf to a teammate while keeping their enemy targeted for attacks. The rest of the time, just get used to confirming your target selection choice with X.) It's worth practicing a bit on your own in an area with low level enemies where there's little else going on so you can see what's happening with the target before trying to get used to it in a dungeon.

Targeting filter:
check one or the other (but not both) of the boxes:
Character Configuration -> Control Settings -> Filters -> Enable Target Cycling
or
Character Configuration -> Control Settings -> Filters -> Enable Customization

The first lets you configure two settings according to whether your weapon is drawn or sheathed. Or the second lets you configure up to four settings you can alternate between manually by pressing L1 + one of the right-side face buttons. (I'd recommend the four manually controlled filters, as it's more versatile, but maybe someone who only plays tank or DPS can do ok with the drawn/sheathed pattern.) Then, for each filter, there's a collection of checkboxes for whether to include players, NPCs, claimed enemies, unclaimed enemies, pets, and so on.

Once you have customized filters, of either type, the left and right controller buttons will cycle only between targets matching your current filter. (If your current filter is one of the named presets like "Friends" "Enemies" or "All", the filter name is shown just above your character's HP Bar to remind you what it's currently on. Otherwise it displays as "Custom".)

Most of the time, I leave my target filter on "Enemies" mode, but I sometimes change it to "All" in town where I may want to inspect someone's cool looking gear or something. When I'm playing healer and running open world FATEs or hunts, I'll use "Friends" mode to target other players not in my party, but I prefer the Up/Down to select party members, so in dungeons, I keep the left/right set to "Enemies" mode since the only friendly players are my party.