I have a Dell Latitude laptop; my battery will generally last about 2+
hrs while on Wi-Fi. I need to figure out a way to increase this time
to 5-6  hrs. Is this possible with the right battery and/or somehow
attaching a second battery that'll automatically kick-in when the
first runs out?

Its not possible with this battery, but it is possible with a battery
pack you assemble or extra packs sold here:
http://www.compusa.com/products/product_info.asp?product_code=341903&pfp=PRODUCTS

You don't need to set up the battery to 'kick in."  The Dell normally
receives 14-20 volts from the converter plugged in.  With a pack that
supplies that amount the unit will either drain both simultaneously or
will switch over when the external voltage drops too low.  I've run my
laptop (a 20 volt, 11amp monster) off of three six volt lead-acid
batteries in the past.  All I needed to do was make sure the plug
polarity was correct.

If you go to http://accessories.us.dell.com/sna/productdetail.aspx?c=us&l=en&cs=19&sku=310-4345
they sell backup battery's that will slide in where your cd\floppy
drive is located.  Pretty standard pricing for a battery Priced at or
around $120

And you can this
http://www.donotebook.com/dell-c613/index.html