Bicycle Tutor

I have a problem with my shifter not "matching" with the derailleur. When chain is in top/high gear (largest sprocket on rear), the shifter says I am in "2" not "1". when I shift the chain down to lowest sprocket it makes it to the 5th sprocket but won't go into the 6th final sprocket. The shifter at this point says I'm in 6th. Of course this makes all the points in between out of sync also.
What part should I be adjusting to correct this? If you need additional info let me know.
- Shimano is the brand shifter and derailleur
- bike is a Diamond back outlook about 11 years old I would think.
- only has about 400-500 miles on it, 300 has been in the last 2 years.

Ok what I did was loosen the rear cable. adjust the hi and lo. seems to have helped. Now I just end up having to give it a little extra push to get it to jump all the way down.