As you own a point and shoot camera (not that it is bad, we all have to start somewhere), I would (if I may) recommend to concentrate on seeing the smaller picture. Great big vistas are a bit hard for a p&s camera to handle properly with the use of filters.
There is landscape work to be found in a smaller scale, start from there and very soon you will be able to recognise and handle (easier) the larger picture. Here are some examples...
All the above images, can be very easily achieved with a p&s camera as your don't have a great depth of field or vast differences in Dynamic range to play with. Just use a tripod which will slow you down and make you concentrate more on the subject. It will make you take less but better images. Finally, make sure your images are simple and uncluttered, less is more.
I hope I am being of help.