Mission Accomplished! Thanks iFixit
My wife spilled a glass over water on her MacBookPro (late 2010 model). After drying it as best we could - without being able to open it - the battery no longer functioned. The device did work with the power cable attached so it was usable although not so convenient. Our local Apple store referred us to local authorized repair vendors since they no longer stock the battery (which they said had a list price of $129 when it was sold by Apple). The nearest repair vendor did not have the battery in stock but could obtain it in 3 days and wanted $200 for the battery installed. We declined but afterwards I looked online, found iFixit, and decided to order it from them. The battery cost $99.95 plus two special screwdrivers and shipping for a total cost of $134.60.
The repair went very well. After fussing over which screwdriver to use, I removed the various sets of screws and removed the back of the MacBookAir and the battery. I then installed the new battery and screwed in the screws which I had removed for the battery and the back of the device. Everything went well and the MacBookAir now functions normally on the battery. Success!!!
For a battery replacement, take heart-- you can do it!
Minor tip to iFixit: Check the labeling on the packages of the screwdrivers and how they are designated in the online instructions. I think that they could be make more similar.