How to mount a curb. (kerb?)

Start with your bike. With enough skill, you can go up a tall curb without damaging the bike. But as a novice, make it easier on yourself.

Remove extra weight: Backpack, panniers, etc.

Remove loose items. Water bottles come to mind.

Flat bars are easier.

Fat tires protect your wheels when you make a mistake.

Prerequisites

It helps if you can ride slowly. If you don't feel confident at below-walking-speeds, then you'll have a harder time learning to mount curbs.

How to do it

The most important thing is to get your body weight off the wheel that is going up the curb. You weigh 5-10x as much as your bike!

Make your approach 90° from the curb. Low speed is good, but make sure you feel stable on the bike. Stand on pedals at 3- and 9-o'clock. Keep your knees slightly bent.

Just before the front wheel hits, throw your weight back and yank up on the handlebars. You may lift the front wheel off the ground slightly, but it's not necessary.

Just before the back wheel hits, throw your weight forward, and hop on the pedals. You may lift the back wheel off the ground, but that's harder than the front wheel. I can't do it!

If you do it perfectly, it should be a smooth motion. The bike doesn't get jolted around. You don't lose any speed.

Where to practice

Try a flat, empty, paved parking lot. You want the biking to be as easy and safe as possible, without distractions.

Before going up a curb, practice with going over a twig or a pebble. See how smoothly you can do it. Graduate to larger items & higher speeds when ready. The concrete bars they put at the end of each parking space can be good practice, too.

Going down a curb

The same principles apply. Before your front wheel drops, shift your weight way back, and ease the wheel down. Before the rear wheel drops, get your weight on the front.

Advanced techniques

If you can bunny hop (I can't), then you can approach a curb or other obstacle at high speed and clear it easily. Good for you.