mae is the main verb in this phrase. It simply means 'is'. In conjunction with the wedi it means 'has/have':
- mae X wedi newid - X has changed
- mae Xs wedi newid - Xs have changed
If you exchange wedi for yn you get:
- mae X yn newid - X is changing
- mae X yn goch - X is red
With no context:
- mae e/hi... - he/she is...
- dw i... - I am...
- rwyt ti... - you are...
It depends what you are looking for. If you intend to keep going with Welsh beyond the limts of this basic course then you could get hold of a copy of 'Welsh Rules' by Heini Gruffudd - a standard and progressive book for Welsh learners which will take you step by step up to an intermediate/advanced level. There is a book of exercises to go with it. It has a good index, too. It covers some dialect variations, which is handy.
More basic is the BBC Welsh grammar guide, if it is still available.