How do I get a block with data to place myself?

Are you looking for how to use /setblock with blocks with data? See this post.

How do I get a block with data in my inventory so I can place it myself? In Java Edition, these commands work:

give @s chest{BlockEntityTag:{Items:[{id:"diamond",count:10b}]}}
give @s sign{BlockEntityTag:{Text1:"{\"text\":\"foo\",\"bold\":true}"}}

How can I do this in Bedrock Edition, where there is no access to NBT tags from commands?

Computers

You can do this with the “pick block” control, which defaults to the middle mouse button. Put your crosshair over the block you want to get and then press Ctrl + pick block, which will put that block with its data into your inventory. Of course, this will only work in creative mode.

Touch devices

Unfortunately, this cannot be done on touch devices without “Full Keyboard Gameplay” enabled, as there is no “pick block” control.

Consoles

Consoles do not have the pick block control assigned by default, and it will have to be configured in the settings window.

For more information on the “pick block” control, see Controls on the Minecraft wiki.