How do I unlock the rotation switch

No details here of your iPad model or installed version of iOS/iPadOS - which may impact the potential solution.

If you have an older model of iPad with a physical side-switch, this is likely to be toggled “on”. Switch-off the side-switch and screen rotation should be fully restored.

For iPad models that incorporate a side-switch, switch behaviour is configurable between locking screen rotation - or muting the iPad:

Settings > General > [Use Side Switch To:] - select either Lock Rotation or Mute

For newer models of iPad without the side-switch, running recent versions of iOS/iPadOS - to enable or disable Screen Rotation, you need to access the Control Centre. Swipe downwards from the top-right corner of the screen - then tap the Screen Rotation lock icon:

If screen rotation proves to be problem with some Apps - and not others - you need to be aware that not all Apps are coded to operate in both Portrait and Landscape screen modes. Apps that have a fixed screen orientation will always* appear in the orientation determined by the App Developer.

(*) For compatible Apps that are intended for iPhone, iPadOS15 will now automatically rotate the App to display in Landscape screen orientation. There is no manual configuration or setting to enable this feature. However, Apps designed for iPad that are expressly coded to force Portrait screen orientation, iPadOS15 will honour the intended Portrait mode. iPadOS15 will not override the App coding.

I hope this information and insight proves to be helpful.