I was given an old Dell laptop that I would like to bring back to life.  I think it last ran Windows 7.  
Is it a project an old dog with very limited computer knowledge can do?  
If so, where do I start or where can I find the info necessary to do it?  
I'd hate to be posting here every 1/2 hour with all my lame questions.

Thanks.

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If it was an Apple I'd recommend you go get help for sure. There are technicians who can work on Apple. But Apple doesn't encourage home repair work and they make opening the case really tricky, so you end up destroying your first machine to find out how it's put together, then the second one you can fix without totally wrecking it. But with Microsoft and compatible machines they're all about being "user friendly" for the fix-it type. Ironically, Apple claims to have a corner on the "user friendly" market but that's only in regards to using the programs, not fixing the hardware. Most good repair guys who can work on IBM compatibles can also work on Apple.
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You have to be sure the hard drive is okay first. A technician can do a check and see pretty easily. If you're real lucky the OS is fine and you just need to charge the battery and turn on the computer. If there is only one broken key on the keyboard, if you want that repaired you're going to have to REPLACE the entire keyboard. This is not uncommon for laptops. You can order a new keyboard. Really.
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Sometimes people get rid of a laptop when the screen goes blank. That might be when the bulb that powers the screen is worn out. That can be repaired but it's not cheap, and could be the reason they didn't want to bother with it. But if that's the only problem getting the bulb replaced is probably a lot less than a new laptop.
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If the drive is okay, then the first thing you should do is wipe it clean and partition it into 3 parts IMHO, and don't use the first part. Only use the second and third parts (one for programs, one for data - the program section can be a lot smaller than the data section in the event you want to store a bunch of family photos or other pictures which use a lot of memory space). Any computer repair guy can do this for you, real cheap. If he doesn't think it's necessary then I guess since he's doing the work and can give you some kind of warranty then you might rather follow his advice. But the reason I say to partition the hard drive is that the first few millimeters of the drive gets written and erased and re-written thousands of times during normal operation over time, and if you can just abandon that section and move over to a newer, unused part of the drive then your system will last a lot longer for you, without any problems. It will be like a new computer.
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Also, check the battery and make sure it is serviceable. If you have to replace the battery it's pretty pricey, usually over $100. So you could be in for three things, 1) new hard drive, 2) new battery, 3) load operating system. That might be more than you want to spend.
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Otherwise, the cheaper route will be 1) HD okay, so wipe, partition, re-install OS,  2) Battery okay, 3) Make sure the cooling ports are clear of dust and animal hair/dander -- requires removing bottom panel and running pipe cleaners through and blowing bottled air or using a vacuum cleaner.  The cooling vents are important to keep the main processor from overheating. The faster they are the hotter they get. Laptops have really cramped space so clear air ports are an essential necessity. When they get clogged the computer gets hot and all kinds of problems result. You should also make sure you have enough RAM or else at least the space to upgrade your RAM in the future if everything else is all right. Otherwise it's not worth spending money on fixing it if it's going to be no good later.
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I got a nice Dell laptop from a neighbor who just got tired of it running slowly. The battery was sort of okay. I had a local repair man wipe the hard drive (it had Windows 8 ) and installed a bootleg copy of Windows 7 Professional. He replaced one memory stick with a more powerful one to give me 4 gigs of RAM.  He checked it all out and said it looked fine. That all cost about 160 and it's been working for 4 years now. But I need to replace the battery. A new computer like this would cost me $500.
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Windows 8 was a dog, a lot like Windows ME was (millennium edition). 8 was the first attempt at touch-screen technology and it didn't work very well. A lot of people who got new computers with 8 got rid of it and bought a new one with 10 instead. Most vendors did not accept trade-ins. Systems (personal computers) running on 8 often had insufficient RAM for the same features in 10, because 10 is a bigger package of goods in the operating system. Some systems allow for more RAM to be added not too expensively and others do not.
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 :o

Where is the spinning head emoticon when I need it!

Lot of info Neil, thank you.

Well... I had hoped there was a magic wand for the process since computers have always worked by magic as far as I could tell

I am actually looking at this as a science project and will take my time to work through it. I have my own laptop that still works fine so this one is truly an educational project. 

The case is fine. Previous owner was a little old lady who kept it on a desk. I do know the battery is shot but it fires up when plugged in. I probably won't replace the battery sine I don't need mobility. 

Thanks!  More entries in my :o notebook.  It will be published under the title  Laptop Revival for the Digitally Impaired.