hi John, here's the links:

https://www.gov.uk/visas-immigration
https://www.visa4uk.fco.gov.uk/
http://www.vfsglobal.co.uk/philippines/

.. I don't know all about your friend's circumstances but everything is done online now, all the links are provided above for your friend to read and understand.

.. Your friend who will turn British Citizen needs to apply an ILE (Indefinite Leave to Enter) visa for her daughter in the Philippines to join and settle with her here in UK.

and yes the process is very straightforward as long as you got all your documents in hand.

Good luck