Installing a garage door opener is one of the easier things a DIYer can do. You don't mess with the door or the springs. Being your doors are made of wood, they are probably heavy, so a 2 horsepower door opener would probably work well. You should not need more than that.
In answer to your questions:
1. Yes 2. Stanley makes a decent one. Chamberlain does too 3. You can do it 4. Don't touch the springs.

Basically, you follow the directions. Put a bracket on the door. Assemble the opener. Raise it into place. And attach it to the ceiling with the provided hangers. Attach the wire for the manual button and run it to a place that is convenient. And plug it in. Assuming you don't have an outlet in the right place, you will have to run some wire and put in an outlet above the opener, but that is not hard either. This would be a good Saturday afternoon project. Just read the directions.

I feel compelled to offer the following comments on this response.

"Installing a garage door opener is one of the easier things a DIYer can do."
Not true. This is not as simple as say hanging a picture. It is not exteremely difficult but does require some skill/mechanical ability.

"You don't mess with the door or the springs."
This is true providing the door/springs are in good shape and are operating properly, including but not limited to; no binding/proper balance, etc.

"Being your doors are made of wood, they are probably heavy, so a 2 horsepower door opener would probably work well. You should not need more than that."
2 horsepower?????? maybe you meant a 1/2 horsepower. The opener doesn't "lift" the door, that's what the springs are for. The opener compensates for the manual effort required to open the door which varies according to the door step up.

in answer to your questions:
"1. Yes"
True, for two separate doors you need two separate units

"2. Stanley makes a decent one. Chamberlain does too"
True. However, there are a number of good manufacturers and types available. FWIW, I've had good luck with Craftsman. You need to choose between chain, screw, or belt drive depending on what you want to spend and how quiet you need it. Also select your options like keyless entry or optional light controls.

"3. You can do it"
change to "maybe" see the attached link for a typical owner's manual that has the installation instructions and decide for yourself.

"4. Don't touch the springs."
As stated above this depends on the condition of your existing hardware.

Basically, you follow the directions. Put a bracket on the door. Assemble the opener. Raise it into place. And attach it to the ceiling with the provided hangers. Attach the wire for the manual button and run it to a place that is convenient. And plug it in."
All new doors have sensors at the base of the door that also require installation and running wires

"Assuming you don't have an outlet in the right place, you will have to run some wire and put in an outlet above the opener, but that is not hard either."
YIKES, a "fairly inexperienced handyman" should probably not be running new electrical lines. Not impossible but do some research and make sure everything is correct.

"This would be a good Saturday afternoon project. Just read the directions."
see the manual and decide for yourself.

FWIW, I'm not a pro and have installed a few of these. You need to recognize your limitations and understand what is involved.
There are some pros who post here fairly frequently. I hope they agree with my advice.

cstrombe: good luck with your new openers!

Here is a link that might be useful: typical owners manual

Installing a GD opener can be a DIY project.
I installed 2 before. My last house and the one before that.
When I bought the opener for my current home. $99 install was too good a deal to pass up. Note: this was for a typical installation (for one door).
At my previous houses,
I can recall spending half a day getting it up and working right.

Anyway, it sounds like you may need help to DIY it. Invite a "handy" friend over. Good luck.

-jasper

Chris if your wife can open these doors without straining they are in good shape and you can add an opener with no problems. I would personally recommend Chamberlain products. Lowes and Home Depot are just a couple places that stock them. If you have single car garages I would buy the 1/3 horsepower if available. No need to pay more. They come with excellent instructions for the DIY'er. Just take your time and follow the instructions step by step. It is a one man job but having a friend around sure doesn't hurt.

Thanks for all the input everyone (keep it coming!). My wife can open them no problem. They are single car doors, so thanks for that tip. Might save us some money to go with the 1/3 hp.

Seems like the chain is the way to go from what I have read elsewhere. We aren't concerned with noise. Any reason to get a screw type or any of the other varieties?

Thanks,
Chris

Chris I would not recommend the screw type and if noise is no problem I would go with the chain drive. Cheaper, dependable and has been around longer than anything else on the market. Your wife will love you the first time she comes home in the rain and uses her opener.

Cstrombe

My only concern is the way you describe the door. It's wood with springs and cable, but then you mention weights.
Is this counterballance weights? Is this a wood, one piece swing up door and are the cables attached to the door at the ends of the door, about half way up? If so, you may not be able to put an opener on these doors.
Are they sectional doors? Please describe the door and the way it works a with a little more detail.

Sorry, I don't know why I mentioned weights. It's a sectional door. No weights. Just springs and pulleys if I recall (I'm not living there yet--just got the house). There are two "single car" sized doors, side by side (with a column separating them).

sdello - sorry I missed the 1/ in front of the 2. My intention was to put in 1/2 horsepower. But geez loueez, are a lawyer or what? You picked apart every single statement - even number 1 - I responded 'yes' but you even had to add a qualifying (and useless) sentence to that. Do you think that the OP was not smart enough to understand 'yes'? I do not equate hanging a picture with being a DIYer. This is a great opportunity for someone to get some DIY experience for a relatively simple project. I suspect you have offered instructions for how to use a leaf rake as well.

If someone asked how to use a leaf rake, I would likely help out and post instructions.