what should i do proper care and extend battery life of one of the ff types:

Li-ion:(uses PSP battery and Laptop battery)
1.)to take care of that Li-ion leave my battery empty(discharged) if unused for a long time????
2.)is it true? if these batteries should NOT always full charged if NOT used for a long time otherwise it might damaged??

Lead-acid battery:(uses UPS that my desktop used for emergency power and emergency lights)
1.)is lead-acid battery will be damaged if remains discharged and/or always FULL charge all the time if unused for a long time?
2.)according to the manual to extend battery life that battery must be drained if unused about 3 months then charged it again.
3.)overcharge this lead-acid will damaged my battery?