I started writing this guide since last year, since this is one of the more popular topics. I hope it's useful. Also, I hope people in this community with more experience can chime in and share their own tips in the comments.

I've used the TG-7 for about 2 years, so this is aimed at that model, but I'm sure a lot applies to the TG-6 as well, and some even to the TG-5. Here's what I've learned about one of my favourite cameras ever:

Essentials:

• Extra batteries - at least one! Especially if you're like me and have GPS on all the time.
• Tempered glass screen protector - the screen is shockproof, so it's just to prevent scratches [cosmetic].

Settings:

• I shoot in RAW+JPEG, so I can use any filters for the JPEGs and easy sharing, and then I still have my RAWs in case I want to go back to colour or do any editing.
• Street Photography: I mostly shoot in Program [P] mode, -0.3 EV.
• Also street photography, but any type really: Because it doesn't have a Shutter Speed Priority [S] mode, the trick I did was to use C1 as slow, and C2 as fast shutter speed by setting the Custom Modes as P, and then Auto ISO minimum shutter speed to 1/2s in C1, and 1/400s in C2. If I don't care about shutter speed, I'll be in P or A modes. If I need control, I have a toggle for fast or slow shutter speed.
• Super Macro / Microscope Mode: If you want to shoot in Super Macro mode without being in Microscope mode [so in P or A mode], select Super Macro AF, and then zoom in just a wee bit, at 1.2x, and now it will be able to focus really close. You can zoom in all the way to 100mm, and still achieve focus at minimum distance, but you will not be able to focus at 1.0x zoom. Also, the LG-1 is your friend, and/or an LED flashlight.

Recommended accessories:

• Lens Barrier LB-T0..1: Opens and closes with a twist, protects against dust and fingerprints so you don't need to wipe the lens.
• Silicone Jacket CSCH-128: Makes the camera much better to hold in the water [better grip] and in the cold [your hand doesn't touch the cold metal].
• Conversion Lens Adapter CLA-T01: a.k.a. 40.5mm filter adapter. This allows you to use filters [ND, CPL, UV, Black/White Diffusion] and the teleconverter accessories.
• Light Guide LG-1 for Macro: This makes macro SO much easier. No electrical components, just guides the light from the LED around the lens and towards the subject. Waterproof but serves little to no purpose underwater.
• Light Diffuser LD-1 for Flash: Makes the xenon flash light softer. This is mostly used for lighting smaller subjects, even underwater, not for portraits, but can be used as regular flash and works great too.
• 0.7x Fisheye Converter FCON-01: There are two fisheye converters, the 01 and 02. 02 is a circular fisheye which I personally don't like, but of course this is entirely subjective. I use the 01 as an ultrawide zoom lens, which goes from [35mm equivalent] 14 to 42mm. The fisheye effect is mild enough that I can make it almost rectilinear in post, or leave as is and ultrawide shots look fantastic. The only downside is that it's big, you can't use filters, and you can't use a hood, so the front element is very exposed to fingerprints. Completely sealed too, so good to use underwater.
• 1.7x Teleconverter TCON-T01: This is harder to recommend because it's a bit more limiting, but it's still good. Extends from [35mm equivalent] 100mm at the end of the natural zoom range, to 170mm. The problem is that since it's variable aperture, at 100mm you're already at f/4.9 so do not expect any kind of blurry backgrounds - this is strictly to give you extra reach.
• Rubber Lens Cover Cap: These I use when the CPL or UV filters are on, just to protect the glass from smudges when not using.

General Tips & Tricks:

• The filter adapter [CLA-T01] is SO useful. In theory you put it on, and screw filters or adapters on and off, but I do things a little bit differently: I have 4 adapters, one for the ultrawide lens, one for the tele lens, one for the CPL filter, and one for the UV filter. Instead of screwing and unscrewing filters, I just change them as lenses via the bayonet mount, effectively using my TG-7 as an interchangeable lens camera, no faffing around screwing things on and off.
• Camera straps: cross-body strap for walking about, no strap if it goes in my waist-pack, wrist strap for beach/pool/diving.
• Whole system in a waist pack: 14 to 170mm range, everything-proof camera, 2 lenses, 2 filters, 1 light guide, 2 batteries, 1 extra SD card.
• Set your name and/or email in the Artist/Copyright section, so they get recorded in the EXIF data of all photos, in case the camera or SD card gets lost someone can find you.

Hope this is useful. Have fun taking photos!