Well, it's not really the answering machine that is dumb, but I AM.
There is a luddite crisis going on here or my ADD is really flaring
up. My telephone answering machine is broken and after 20 years, it
doesn't make sense to repair it. I have a terrible time understanding
directions and am desperate to know which newer  answering machine is
not only a reliable one, but which one has the easiest directions to
understand how to use. DIRECTIONS DRIVE ME NUTS!
The only thing that I know how to do on the computer is use the
Internet and that is because I use AOL, which every one knows is for
DUMMIES.(This is one of those times that I could use a smart eight
year old around the house.)Please help!
Thanks,
Yesmam

Howdy, yesmam!

Stand-alone answering machines that are relatively simple seem to be
headed for extinction, but I found descriptions of some units that I
hope will meet your needs. Here are some answering machines that sound
as if they don't resemble rocket science in their learning-curves:

"I used this answering machine to replace my $8 a month voice-mail
from the phone company. I have no major complaints from this great
product, and it's even a cool looking see-through blue. Very easy to
set up and operate, and I was pleasantly surprised that accessing
messages remotely is as easy as with voice-mail. Very intuitive
voice-prompted instructions on how to skip, delete, or save messages."

GeoReviews: Casio TA114 Digital Answering Machine
http://www.georeviews.com/Casio-TA114-Digital-Answering-Machine_L50261/

"Offers a no-fuss way to receive calls while you're busy or not at
home. It's simple to use, and holds up to 8 minutes of record time.
Listen to messages from a touch-tone phone when away from the house,
and there's no tape to replace!"

TWA at Home: General Electric Digital Answering Machine
http://www.twaathome.com/Catalog/Model_GE-29888GE1.htm

"The AT&T 1717 is a tiny answering machine, so it takes up little desk
space. It's extremely easy to use, whether recording an outgoing
message or playing back incoming messages. Setting the day/time is
easy as well. It's the kind of answering machine that your non-techie
grandma would have no problem using. I don't use other features like
any of the remote possibilities: room monitoring, turning the machine
off/on, recording new messages. If I haven't made it clear, all I want
is something that will answer the phone and record messages without
mangling them or losing them.

The bottom line is that it is a very simple answering machine. It's
easy to use and has acceptable sound quality. One can screen calls,
selectively save or delete them, skip or replay messages, and attach a
time/day stamp to messages. It's capable of recording up to 12 minutes
(which would be an exhaustive amount of messages). Unless some one is
unusually fussy or has special requirements, I'd recommend this as a
solid little answering machine."

Epinions: AT&T 1717 Digital Answering Machine
http://www.epinions.com/elec-review-656-2745D12F-3A21EED3-prod5

"Intuitive, not bulky, clear... I got this answering machine as a
gift, and I've really like it. 100% better than my old static
recorder! It's very intuitive... I think this is a good answering
machine for anyone who does not like to read instruction manuals. The
only thing you have to look in the manual for is your remote access
code."

Epinions: Panasonic KX TM100 Digital Answering Machine
http://www.epinions.com/elec-review-5DB7-35CD3252-3A0FFAE1-prod6

This last one is much higher in price, but the description and the
photo of the unit (scroll down the page to see it) are very appealing
to me, as a fumble-fingered person with a hearing loss. GREAT BIG OL'
BUTTONS. Yay!

"The Easy Recall Answering Machine from Ameriphone provides a powerful
amplifier together with a high fidelity speaker, which produce loud
and clear sound, without any distortion, so you can hear every word. 
Adjustable Tone Control lets you hear and distinguish between similar
sounding words, so you'll have no more unclear messages.  Provides
large, easy-to-see buttons for simple operation."

Just Bekuz: Telephone Amplifiers
http://www.justbekuz.com/telephones_amplifiers.htm

Google Web Search: "answering machine" "simple to use" -software
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22answering+machine%22+%22simple+to+use%22+-software

Google Web Search: "answering machine" "easy to use" -software
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22answering+machine%22+%22easy+to+use%22+-software]

Google Web Search: "answering machine" "ease of use" -software
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22answering+machine%22+%22ease+of+use%22+-software

I hope I'm on the right track here. If one of these sounds good to
you, I'll be glad to go on a hunt for a good price online. Just let me
know. I was hoping to find a "Hello Kitty" answering machine, but
apparently that market hasn't been tapped yet. ;-)
 
Best,
Pink

HIYA PINK-OL' BUDDY! Once again, you've come to my rescue. You've
provided many good links to start my exploration and I appreciate your
great work as usual. With goofy electronics these days, they probably
do have a "Hello Kitty" model, but I wont look into it because I'm not
going to be upstaged by a vacuous feline with no mouth.
If God would grant me one wish, it would be the ability to understand directions.
Thanks again Pink,
Yesmam

You could also add digital voicemail service courtesy of your local
telephone company.
 It's usually as simple as dialing a special # to check for messages,
then pressing a key to listen, another key to save, and yet another to
delete.

Thank you muchly for the five-star rating and the nice tip! 

The comment above by pcventures-ga is an excellent suggestion. My mom
has been using the local phone company's voicemail for quite a while,
and she seems to be quite pleased by it. This very sharp but extremely
Ludditic woman has not yet figured out how to program a VCR nor how to
set an electronic alarm clock; if she can work Ma Bell's voicemail
system and not have to ask me questions about it every few days,
that's an impressive sign that the service is easy to use.

~Pink

Now, this idea of turning the telephone into an answering machine
sounds great. Thanks so much pcventures.
On the subject of Ludditic mothers, I'm going to revamp my old laptop
and teach my mother the Internet for Christmas. My father has started
teasing me and saying that my intention is to go for the Nobel Peace
Prize, but it might be akin to going into battle to receive the
"Purple Heart." My dear ol' Ma is worse with technology than I
am."Fasten your seatbelts!"
Pink, if we don't chat before the holiday, have a happy one.
Thanks again,
Yesmam