I use popsicle sticks, otherwise known as 'craft sticks' at Michaels, for the basic material. For my weathering agent, I utilize a solution made from india ink and rubbing alcohol; that's a trick I picked up from my model railroading buddies.
The truck in the foreground has the ink/alcohol stained wood:
I also used a few of my weathered boards for the floor atop this deuce frame:
I keep the ink mix in a 'reassigned' pickle jar, and the soaking vat is a topless Tupperware container. The soak time is usually between 10 and 20 minutes, and I let the pieces air dry on paper towels or newspaper overnight....although drying in the sun can help speed up that process. A small number of boards in each batch are re-dipped, and some are faded by dry sanding, to give the bunch some color variation - in real life, not every piece of wood ages at the same rate as others.
My preferred method of application is dipping, but I have had good results from applying it with a dropper or thick brush.