All that.
Be careful running your finger/thumb around inside the tyre because sometimes, you find the problem by ripping a chunk out of said digit.

Sometimes, you'll get a bit of glass stuck in the tyre and while it pokes through when under pressure, doesn't poke through when not. Find the hole in the tube. Lay it over the tyre, look inside AND outside the tyre for a problem (from the outside, you may only see a small cut in the tyre). This is where lining the badge on the tyre over the valve helps as it gives a guide to how the tube and the tyre fit together.

When you find the hole in your tube, have a close look to make sure the hole is not on the inside of the tube (when installed) - it's not unknown for the holes in your rim that take the spokes to cut the tube.

Seriously though. LEARN HOW TO FIX TYRES YOURSELF. This is basic mate. It's not rocket science and it's the most common repair needed on the side of the road. Paying someone to fix flats is like paying someone to squirt lube on your chain.