Monte to Curral dos Romeiros
From the Monte cable car terminal (to Funchal), walk towards the other terminal (for the Botanic Garden). The path will split with part going downhill - this is the route you should follow (on the right in the picture below).
At this point, parts of the path are quite exposed, so be prepared for the weather you may encounter. There are some deceptive brief descents, but from here on the path is largely an uphill climb.