Describe the trend of physical properties of main sequence stars on the H-R Diagram?

Question

(from the lower right to upper left)

Answer 1

Cool and dim and red in the lower right to hot and bright and white/blue in the upper left.

Answer 2

This depends on how the H-R Diagram is organized- there are several different layouts.  

Arbitrarily picking a layout...

If the "x" axis (to the right) is color and the "y" axis (upward) is brightness, then the lower left corner represents cool-red stars and the upper right represents hot-white ones.  The "Main sequence" of stars, that is, the place on the diagram where each star spends the majority of its life, is roughly along this lower-left/upper right diagonal.    

Some properties, as one moves from lower left to upper right along the main-sequence:

- stars become more massive

- stars live shorter lives (like James Dean: "live fast, die  young", but, in the case of stars, it's live bright, die young")

- They tend to become bigger

Once stars leave the main sequence, however, all bets are off:

- Bright-red stars (upper left) are giants, and are at the end of their lives.  Many of these are in the process of making elements heavier than Helium.

- Dim white stars (lower right) are white dwarfs and neutron stars.  They've largely finished with fusion, and have compressed down into exceptionally dense bodies.  They are very hot, but not very bright because of their small size.