Is this a plain 110, or a 110+? The battery replacement procedure is slightly different.
The plain 110 is the easier one. Unclip the cover on the back, disconnect the 3-wire cable (battery and reset button) from the little PCB. Remove the 2 Torx-head screws and the cover over said PCB, then slide out the battery and PCB. Most machines have a Panasonic 'block battery' in them, but if this is hard to obtain, 3 2.5Ah Cyclon cells wired in series fit and work perfectly. Take care to get the polarity correct!
The 110+ has a similar battery, but it's connected by metal strips held on by nuts. The official HP procedure involves bending those strips, and you're supposed to replace them every time. They are, of course, unobtainable now.
So what I do is : Unclip the cover on the back, move the battery link to the 'off' position. Take out both drawers. Remove the cover over the battery terminals (2 screws), then take off the nuts on the battery terminals and loosen those holding the strips to the main PCB. Take out all the case screws on the bottom (Maybe some under labels). With the machine the right way up, free the connector strips from the battery terminals, then separate the case halves starting at the back. Reach inside and unplug the display and keyboard cables. Turn the top case over, take out the 4 screws in the hinge posts that hold the cover over the battery. Remove this cover and the battery is easy to get out. Again 3 2.5Ah Cyclon cells in series are a suitable replacement. And again take care with the polarity.