Click the ellipsis to the right of the App you want to share open the dropdown, and select "Share"

Click "Share"

Select a SINGLE USER that you want to share the app with 

Select the user to share with

On the bottom right of that dialog window, you will see a dropdown next to each asset that will be shared along with the app itself. 

open the drop down

Open the dropdown and at the top of the dropdown you will see a link for "Manage Security Roles"

Click "Manage Security Roles"

Click through the link and scroll through the roles for the desired role that you want to assign to the table and share. 

Select Role to assign permissions to

I've used "Basic User" in this example as it will be automatically shared with any users that you share the app with. 

Click the Name of the role to continue. 

Inside the Role Menu, click the far-right tab called "Custom Entities" 

All of your custom entities will be listed under this tab

Find the name of the table you want to share along with the App and select the permissions you want to share. NOTE: at the very least you will need to share "Read"

Find your table and select permissions

Go up to the top of the screen and select "Save and Close" 

Go back to the tab you had the share dialog open in and click "Share"

Congrats!

If all of these steps are done correctly, the user selected, should now be able to at least read from the shared table. 



Alternatively Go to the admin center in PowerApps. 

Select the row and then click edit. 

Find the table you want to share and give it the appropriate permissions.