Hello and welcome to my User Tip
If you want the maximum RAM your machine can hold you need to do it yourself (and save a bundle too)
Some Mac's like the non-Retina MacBook Pro's, and MacPro one can upgrade the storage without violating their AppleCare/Warranty if nothing is broken in the process.
The 2011 iMac's and later have proprietary Apple software installed to talk to OS X to control the fans, so Apple will have to upgrade the storage or call OtherWorld Computing as they have a hardware solution.
Check out this Apple support document so you know where to touch the Mac to discharge static electricity.
Some Mac's can accept MORE RAM than Apple says, read on below.
1: Apple Menu > About this Mac > More information, look for a "MacBook Pro 3,1" or similar.
2: Install the free MacTracker, then find your machine and it's true RAM capacity also find out it's internal connection speed either SATA 1, 2 or 3.
3: Call or visit OtherWorld Computing, Kingston or Crucial.com, or another very reputable Mac RAM vendor and find your machine, they will match the correct RAM specifications and amount. You really do not want to be opening the machine more than once, so well tested RAM is important, as shipping it back is a hassle.
4: Visit these install videos and buy the needed small tools (no substitutes) to install the RAM or internal storage drive yourself.
The tools MUST fit the screw heads perfectly because the screws are tiny and a slightly mismatched tool will STRIP THE HEADS!
Search YouTube for RAM install videos as well.
5: Make sure to read up on proper anti-static behavior and don't touch the RAM contacts (or any electronics), just the plastic edges.
Place each screw into a plastic compartment so it goes back into the same exact hole it came out of.
Another trick is to have a large surface and place each screw in a position near where it came out of the machine as show in the picture.
Notice one can see the very tiny screws easily against the tan colored sheet.
Don't carry the small screws where there they can be dropped inside the machine or on the floor, they tend to disappear easily and are very hard to find. I find it was easier to position the screw between two fingers and place it into the hole, then follow up with the perfectly fitting micro screwdriver.
5.5. For upgrading storage, I recommend SSD's on SATA 3 connections cheifly, SATA 2 less and really not at all on SATA 1 because usually the machine is rather dated by then and almost due for a major hardware failure. A 7,200 RPM hard drive for SATA 1 and possibly even some SATA 2 machines might be more cost effective and provide more storage.
5.6. SSD's can't be securely erased, so if you require secure erase ability in Disk Utility, you will need a hard drive instead.
6: If you choose a GOOD RAM vendor, 99% of the time the RAM will function perfectly the first time, if you go cheap, used, backalley or no-name, it will fail up to 99% of the time and the seller may not talk to you anymore, disappear or keep sending you crappy RAM.
7: Do not strip the screws heads using the wrong sized tools, the right tool will fit the screw head perfectly. Don't go fiddling around taking other things apart, as only RAM and Storage replacements are acceptable, you open anything else or break it, it's not covered in the warranty or AppleCare.
If there is a problem with screw not coming out, then take it to Apple and explain the problem.
Do not force strip the screw head and use the exact fitting tool for maximum leverage.
If you strip the screw head that's not a warranty or AppleCare covered item, it's user inflicted damage.
8: Use a magnetic pickup tool or screwdriver and aim directly for fallen screws in tight places. Last resort should be turning the machine over onto a mat to see the tiny screws when they fall out. Better to hold the screw in a manner that it doesn't fall into tight spaces or dropped where it possibly can't be found (like on the floor or carpet)
9: Seat the new RAM fully into the slot until the arms close down.
10: New storage or RAM is not covered by warranty/AppleCare.
11: If you later suspect your new RAM is faulty, it will show by Kernel Panics (You need to restart) or machine freezes.
12: Do not throw away or trade your old factory RAM, as you may need it if the new RAM is not good or have to trade the machine in at Apple for some reason for a new one.
13: You can "test" the RAM with a extended overnight test with the free Rember program.
14: Whatever you do, make sure to enter the insides of the machine as least as possible and touch nothing if possible.
15: If it's a older MBP out of AppleCare or warranty, I would investigate cleaning the exhaust grill where it exits the machine behind the fans, to clean it of clogged dust, lint and hair. This may require removing the fans, at your own risk of course.
16: Never allow liquids inside the machine, a gentle toothbrush and perhaps a blast of canned air (no freezing or condensation drips) There are moisture sensors inside the machine.
Good Luck, it's a LOT easier that what I made it out to be and sounds more scary than it truly is.
note, a work in progress.