You will realize the greatest savings on expensive parts that require little time to install, such as a brake caliper or an alternator, which could take less than one hour to install. To find out how long a part will take to install, go online (to sites like AutoMD.com) where you can get a difficulty rating on your part installation and the average number of hours a mechanic should take to install the part. While you are there, check out the labor rates at your local shop, so you can fully calculate the job cost. Then compare prices at online parts sites to find the best price on your part. Also, when you check with your mechanic to see if he will install parts purchased elsewhere, ask him to provide an estimate of labor hours to install your part and if he will match the price of the part you plan to purchase.
If the repair requires an inexpensive part, like a thermostat, or the job is labor intensive and the risk of part failure outweighs the cost savings, let the shop supply the part.