Here is a step by step tutorial, assuming you have the latest version (1.16.40) of Minecraft Bedrock Edition.

First, you enter the profile screen by clicking the profile button on the main menu: There is room for five character slots, each being highly customizable. Cycle the active character using the < and > buttons, and press the Edit Character button (highlighted below) to enter the editor:

Now it is time to talk about the different types of skins in Minecraft Bedrock. There are two styles of skin in Minecraft Bedrock: ones made in the character creator and classic skins. Classic skins are simply image files that are wrapped around the 3D object, for example, here is the image file for a chest:

Skins created in the character creator are newer. With them, you stylize your character like you are playing a Dress Me Up-style game, by setting different hats, eyewear, clothing, etc.

Which type of character would you like? Scroll to the section that best suits you.

Character creator

To choose the character creator, click on the first tab in the editor:

Then choose attributes under the "Body" or "Style" headings to modify. You may then choose new styles to add to your character.

• Items with a green flare in the top left are new. You have not seen them yet. The green flare goes away when you view the item.
• Items with a silver lock require an achievement to be collected in survival mode with cheats off in order to use them.
• Items with a gold circle in the bottom right represent paid items. Click on them to view the price, in Minecoins. You can click the Minecoins button at the top right of your screen to buy Minecoins directly, or you can use real money to pay by clicking the corresponding button.
• Items with a blue downwards arrow in the bottom right mean that they are available for free, but not downloaded to your files yet. You can select them and download them from the Internet to use them.

Scroll down further to look at info on emotes and capes.

Classic Skins

By default, the game does not come with any classic skins available from Minecraft and Microsoft themselves. However, many Minecraft Marketplace creators have come up with skin packs, which are a collection of skins following a certain theme.

To use a classic skin, click on the second tab in the editor:

• The "Owned" heading is a list of classic skins you currently own.
• The "Get More" heading is an endless list of skin packs. You can view more skin packs and search for them in the Minecraft Marketplace accessible from the main menu. When purchasing a skin, you in reality are purchasing the entire skin pack with it.
• The "Realms Plus" heading is another endless list of skin packs available through a Realms Plus subscription.

Emotes

Click on the third tab in the editor to get to the emotes tab. There are six slots available for a character's emotes, accessible in-game by pressing B in game, or the left button/dPad-left on your controller.

Click on a slot to see the possible emotes, and click an emote to assign it to that slot. The same flares and icons as in "Character Creator" apply.

Please comment if this answer becomes outdated. I'd be happy to update it.