The cost for one sample is $30 as of March 2016. This may not be the cheapest test available, but I would recommend a DEP certified lab. You can use your own sealable, clean one liter container (approx. 1 quart) with a large mouth or ask the lab for a sampling container. The lab recommended keeping the sample refrigerated (or on ice) but this isn’t required.
A download link for a listing of the labs is located near the bottom of the page under the “Test Your Water for Lead” bullet point.
The procedures are in a pdf link about a quarter of the way down the page under LCR MONITORING. The document is called Lead and Copper Tap Homeowner Sampling Procedures (PDF)
One item I disagree with in the instructions: Item #3 says if you have water softeners on your taps, you should use a tap without the water softener. I believe you should test the taps that you use most often for drinking or cooking water; usually the kitchen tap. Testing after the water softener is a true test of the water you are consuming. I have a water softener and plan on testing the kitchen tap.
I AGREE you should leave the aerator on the tap. If you don’t know what an aerator is, then don’t worry about it for the first sample. If results come back high, then we can talk.
I highly recommend downloading the PDF of the Consumer Guide for Lead in Drinking Water