I like using generic petroleum jelly (dollar store Vaseline) and large cotton balls and empty toilet paper rolls, thanks to this forum.
I get the large size container, since it's so cheap, and set it in about 1/2-inch almost-boiling water in a pan at home (you don't want to melt the plastic container). Wait for the entire container's contents to "liquifiy" and then take some needle-nose pliers (or multitool) and dip each large-size cottonball into the vaseline, then stuff them into the used toilet paper rolls. Once each t.p. roll is filled, I wrap the roll, lengthwise, with masking tape so none of the cotton balls fall out. These things burn forever to get some wood going up in flames. Especially useful for damp/wet wood.
I like to fill a gallon-size Ziploc baggie with these. Extremely cheap, extremely lightweight, extremely useful, waterproof, and works fantastic. Better than any off-the-shelf firestarter that I've ever used (Duraflame and Coleman brands). The cardboard of the t.p. rolls will eventually be soaked with petroleum jelly from the inside, hence the Ziplock baggie. I like to use my pliers from my multi-tool to take them out of the bag and place in fire pit. Dual-use also, since now you have a source of Vaseline for cracked lips or knuckles or whatever for emergency reasons.
For car camping, I like to have 2 to 6 half-egg-cartons filled with dryer lint handy also, since the cottonball method takes more time to prepare. Simply put a squirt of Ronsonol lighter fluid (that I use in my Zippo) on the lint at time of fire, and let her rip. Also lightweight. I store these in gallon Ziplock baggies also so I don't have lint all over in a tote.
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P.S. I wouldn't recommend only using lighter fluid. I've found that I use a lot sometimes trying to get a fire going and stay lit, especially with damp/wet fire wood -- And lighter fluid is pricey!
For fire-building, find some twigs and build a teepee with an opening for to place/light the firestarter, then get it lit, then add some larger wood. I like to find a large fallen tree limb or 2 (this is where digging a hole comes in handy) and place on top lastly (with the middle of limb(s) in the fire, preferably 2 limbs to make a "+") -- even if it's 20ft long -- The fire will "cut" the limb for you. I like to dig a "dome" fire pit when camping primitively, as this lets more oxygen under the fire, versus a dug out hole with completely vertical sides. Some people make holes in the dirt around the firepit -- I've yet to do this.
Tip: Teepee fires burn wood quicker than "log cabin" style fires. There's a hundred different ways to stack wood in a fire for different purposes -- Google them. I like to use a teepee/log-cabin hybrid fire. Here's one link with a few architectures listed:
http://en.Wikipedia.org/wiki/Campfire
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P.P.S. Be sure to extinguish the fire totally with dirt or sand or water before hitting the hay sack, especially with those long limbs. This is another reason why I like the Vaseline cotton ball method for restarting a damp fire pit in the mornings, since they're waterproof and burn a long time. Finally, make sure the fire pit isn't "hot" when leaving the campsite -- I wonder how many critters have burned their paws/hooves/talons from some hot dirt or sand covering a fire pit -- Try to overdose it with water before covering back up with soil and/or sand before you permanently leave the campsite.
Happy fire starting!