battery charging

how can I charge 12 v 1.3 amh lead acid battery and use it at same time to power arduino

You need a charger for the lead acid battery. Those may not be over-charged.

The Arduino can be powered with a dc-dc converter. Either with the battery being charged or not, that doesn't matter, those dc-dc converters have a large input voltage range.

tejveer:
how can I charge 12 v 1.3 amh lead acid battery and use it at same time to power arduino

If the only load is the Arduino then a low current trickle charge is all that is needed,
and when the power fails the battery will take over. Thus you can charge with
a current and voltage limit.

If there is a heavier load then a more intelligent charger is probably needed that can
charge at constant voltage with a larger current limit, backing off to trickle charge
based on observed state-of-charge.

12V LA's are normally charged to a maximum of 13.8V (for instance automotive
batteries are typically done this way). However automotive batteries are normally
free to out-gas if overcharged, whereas sealed lead-acid are less tolerant of over-charge
and the gas-generation it causes.

Would something like this work for him?

http://www.ebay.com/itm/RECHARGEABLE-6V-SEALED-LEAD-ACID-BATTERY-DC7-2V-1-0A-/171096366355?pt=Battery_Chargers&hash=item27d6235d13