My Macbook Pro is running Leopard 10.5.8 and I want to install Mountain Lion

Question

What are the steps for doing this?
I bought a used Macbook Pro (late 2008-2009 silveraluminum 250 GB HD model) after recently buying a new Macbook Air that I broke. My Macbook air was a 2012 and came with Mountain Lion 10.8 preinstalled (as there are no CD slots on the Air models). I do have an external hard drive and I had been using that as my time machine backup. Consequently, my entire  Macintosh HD has been cloned from my Macbook Air onto my western digital external HD. However, I cannot restore from my time machine backup (external HD because it says that I do not have the same operating system currently installed on my laptop.
What do I need to upgrade to the newest Mountain Lion operating system? Do I have to buy snow leopard and then again mountain lion? That seems pretty ridiculous. Or, is it possible to just buy the mountain lion OS from the app store or buy the installation CD?
Another question, is I do not see the App store icon on my dock when I have my desktop up. How would I buy Mtn Lion if I cannot access App store. Does Leopard not have an app store app??
Please provide links where I can find necessary software updates and steps to take to get mtn lion so that I can transfer my clone HD off my external hard drive to my laptop I just bought.

Answer 1

First you have to get the Model Identifier from System Profiler, then make sure of it's model and RAM amount, then use Crucial.com or OtherWorld Computing and max out it's RAM capacity.
There is a 10.5 version of MacTracker here that can assist in getting the full RAM capacity of the machine, not just the amount Apple provides, and the RAM specs.
http://mactracker.ca/archive.html
Install/upgrade RAM or storage drive in Mac's
Also a machine that daed is likely got a dying boot hard drive, so you should replace that also with something like a 7,200 RPM for better performance, large storage capacity and decent price. A SSD would be price overkill for that older machine and add another level of problems enabling TRIM support etc.
Next you need the 10.6 white retail disk Apple sells online.
Next you follow this User Tip for installing 10.6 on the new drive. It is advised to Zero Erase the entire drive regardless of new or the old one.
How to erase and install Snow Leopard 10.6
Once 10.6 is installed you use the 10.5 disks to install your free iLife, then use Software Update repeatly until clear to get to 10.6.8 which provides AppStore for 10.8 install (paid).
Now comes the problem. Later OS X verisons of 10.7+ are better on MacBook Pro's Early 2011 and later, the performance drops off if you use machines earlier than 2010 models.
It's because 10.6.8 was written to be a performance oriented with a small memory footprint thus it's better in tune with the processors and graphics potential of the models in it's day.
10.7+ are fully 64 bit operating systems and require a heft bed of RAM, 4GB minimal and a lot more preferred., it's why I provided the MacTracker info so you can put the maximum RAM into the machine and a faster boot drive, with RAM it's usually MORE can be put in than Apple specifies.
If you can think you can live without 10.7+, then by all means enjoy the performance 10.6.8 gives, at least with that version of OS X you can stick with the hardware that came with the machine.  For Snow Leopard Speed Freaks
I say this because a 2008/2009 machine is  5 years old and on it's deathbed far a laptops typically go, so it doesn't have much left in it. It's cooling fins are likely clogged with dust (behind the fans) it's been overheating with the previous owner, the Superdrive is likley worn out and they sold it for a good reason, like that it was going to need a lot of upgrading to bring it to 10.8 only to have 10.9 released in a few months and it will be behind again, or denied being allowed to go to 10.9 or later by Apple due to the age of the machine and unsupported graphics or other reason.
Buying that machine for 10.8+ was not a good choice because of the upgrades required and the poor CPU/GPU performance. It wil run 10.8 of course, just not as snappy as 10.6.8 will be or 10.8 was on your Macbook Air.
If you can live without iCloud, 10.6.8 has over 25% market share still and Apple is issuing security updates but they don't change the version number any longer or give new features.
By the time Apple stops issuing security updates for 10.6.8, that machine likely will be dead of another cause/hardware failure of some sort, most likely the graphics will go on it next.
So I foresee the two events accuring about the same time for you, I see spending more money on that old machine in new software for 10.8 etc., as a complete and utter waste.
If you purchased a used Early 2011 model or later, then I wouldn't have any objection and say go right to 10.8 if it has enough RAM.
OS X 10.4/10.5 need to upgrade, 10.6.8 ok still