I recently sold my lifted Samurai and purchased a very clean 97 Sidekick JX 4DR 4x4 with automatic transmission and 16 valve engine. It has 153,00 miles. The truck seems to run great. I will be using it as my daily driver to save fuel instead of my LX450

On the drivers side of the shift lever there is a little button that slides forward and rearward. I cannot feel or see any effect when I push this button. What is this for?

When I start up I see a light on the dash that briefly says overdrive Off. This turns off when the car is running. As i accellerate, I hear(and see on the tachometer) the transmission shift 3 times. Is the overdrive working properly? My tachometer says approximately 3400 rpm at 70mph.

Is there a link to an online service manual and owners  manual for my vehicle?

What kind of fuel economy can I expect from a stock Sidekick like mine?

Does anyone here know the answers to my question?

The button that's normally on most automatic shifters is either overdrive on/off or perhaps a sport/normal mode so that it will hold the gear for longer for more acceleration.

It should only shift 3 times once you're rolling, which would put you into 4th gear (4-speed auto is probably what it is).

If you are talking about the button on the side of the shift lever, it is the overdrive button.  when you are driving & you push the button & let go, the o/d off light should come on.  To the right of the shift lever should be a rocker switch with  n a/t p   on it.  you should leave it on "n"  if you switch to "p", the tranny will shift at a higher rpm for more power & worse gas mileage.The word " power" should also light up on the dash.   I'll use it to merge onto a freeway during rush hour.Your shifting sounds correct as crikeymike described. 3400 at 70mph seems high, but i'll have to check that on my way home.  I get 21mpg around town & 25 on the highway in my '92 4 door JX that also has the 16v engine.  If you do find an online service manual.... let me know about it.

I have a '95 Sidekick, manual transmission, so my mileage runs a bit better - around 23-25 in town, and as much as 30 on the highway.  I've got about 125K mileage on it.

As for the manual - you might want to check Goodwill stores - some of them even put their books online.  It's amazing what you can find for $4.99.

Online Service manuals

http://www.suzukiinfo.com