Hi!

I´m trying to figure out how to make my laptop LiIon battery last longer. I´ve been searching the internet, but the information is very varied. Some say it´s best NOT to discharge the battery completely, others say I should use the 40%-80% range, and again others say I should charge and discharge the battery completely on regular basis. Why are there so many different suggestions?

What you really ought to consider is a multi-cell battery for a laptop.
Some are only three cell, others are four or six sells. When I switched to a 9-cell battery for My Thinkpad T-60, my world changed for the better.
As for your question, most actual tests show it is best to totally discharge the battery periodically, then recharge it. Otherwise you run into problems of battery "memory" where it has a difficult time creating a full charge after a period of partial charges.

Different technologies

NiCd tend to have 'memory' and need deep recycling
Lithium-ion batteries (sometimes abbreviated Li-ion batteries) do not exhibit memory effects
A nickel-metal hydride battery, abbreviated NiMH are better than NiCd

Thank you for your comments. I have a 9-cell Li-ion battery, and I´ve also read that this kind of battery doesn´t present memory effects. The weird thing is that the different opinions I talked about,

are all comments about Li-ion batteries. So my question is how can I take care of my Li-ion battery?

Take care of it by using it only when you need it. Occasionally fully discharge and recharge it, while remembering that every discharge is counted by a chip inside the battery on most laptop batteries.
Remember that some batteries only last 6 to 9 months, and very few last longer than a year... but that some have been known to last 2.5 years.
Batteries suffer from extreme cold and extreme hot temperatures, so do not leave them in you car. Treat the battery with the same care you treat your laptop.

OK, that sounds reasonable. Now I have to more questions about batteries:

1. My laptop comes with a small program called SmartBattery, which can be configured to charge only 50% or 75% of full battery capacity. Does this make any sense? Will it make my battery last longer?

2. Will my battery charge faster if I turn of my computer while charging? And should I take out the battery when it´s fully charged, or will the computer automatically stop charging at 100%?

no and no.
smart: it signals the processor on it's status. personally never seen one to control
the amount of charge given -- just monitors charge status
yes, laptop charging is efficient. I leave my installed.

All studies and lab tests say No, for the most part.
When somebody comes up with something that will work, the world will beat a pathway to their door.