I'd say that at about 40 reading glasses are par for the course. I'm glad you've decided to get an exam, too. That will resolve your needs.

My advice on glasses:
I have reading glasses and sometimes need for distance too. I've found that no-line bifocals work great with the computer and still let me see the keyboard and paper work. You really don't want to have to take your glasses on and off while you're working.

For just reading, I found the $20 reading glasses at the drug store work just fin. In fact, they match my prescription (+1) and the DR. said "go for it, save the money." This is good as I tend to loose them regularly and step on them and such. Cheep is a good thing.

And cheaper is a better thing. I used to buy my reading glasses at the 99 cent store. I'd buy them 10 at a time because I'd always lose them. Now they've gone up to $1.50 a pair. When I started out (late 40s) the weakest (100 diopters, if I'm using the correct unit) were fine. Now I'm up to the 350s. When I had my eye exam (good to have once a year) my doctor also said the cheap-os were fine.

If reading glasses aren't helping, you probably have more than just the retinal stiffness that sets in around 40, like maybe an astigmatism, or maybe you just need a prescription that's much sharper than the +1s and +2s the reading glasses generally are (for instance, my nearsightedness prescription is 7.5. They don't make reading glasses that powerful!)

None of this is a big deal. Go to your eye exam and bring up all these questions with the optometrist. Then you get the fun of picking out frames. It's possible to just get your prescription from the eye doc and then order the lenses and frames online, for cheaper. But I like trying them on, a lot of them, so I usually just get them at the optician's store.

p.s. - they'll ask you in the exam how you use your eyes (computer screen, reading, birdspotting, etc) and they'll also ask you about your lifestyle (do you drive at night, have kids, play sports) so that you can choose lenses, coatings, fits, and frame styles that suit your needs exactly. Also, don't get your heart set on a certain shape or style of frames until you learn your prescription. The prescription really determines what frame shapes and sizes your lens can be cut to fit. A lot of the glasses I love are ones I'm not able to wear, because my coke-bottle lens thickness won't fit in the frame (even ultralight lenses are thick at the edges).

Oh honey happens to many of us! I have to wear glasses to work on the computer or to watch TV - for some reason lit screens are my weakness.

It is not an inexpensive option; but so help me; the modern large flatscreen TV was made for being a giant computer monitor.
In lieu of reading/working on the screen for hours with an 18" away focal point, it allows you to have a focal point of 3-4 feet; and it makes for a hell of a video screen too. No more feeling dizzy or intoxicated from crossed eyes when I step outside.
I always thought the large screens were extravagent items until I and my poor vision had one in the home. FWIW, it is another office tool now; and if I itemized I'd use it as a write off for taxes. Computer screen.

There is a really excellent webpage that discusses how one's eyes change as you age.
This happens to EVERYONE over 40 - just a little faster or slower as people vary in their aging process. My SO has varifocals, which take a while to adjust to. I just have long-distance specs as I can read OK without glasses. But more recently, my optician recommended that I get some "mid-range" specs for working at the computer, as I could not focus well on text at an arm's length distance. They make a lot of (positive) difference, when I work at the PC for long hours! Like buzzman, I also bought a larger monitor(!).
You need to see an opthalmic optician for a good eye exam. But you can get the prescription filled at one of the high street chain stores. I always get mine from SpecsSavers in the UK, when I go back to visit, as they have good opticians working for the chain. You can get the same sort of two-for-the-price-of-one deal in the US.

I am short-sighted and have astigmatism. I've worn glasses since I was 16. A few months ago, I had an eye test and was told that my prescription had changed quite a bit (time of life etc). The optometrist suggested multi-focals, but I decided I'm not old enough for that (plus the initial nausea, blind spots etc). I decided to get (when I can scrape up the money) a pair of single-vision glasses for closer work and a pair of prescription sunglasses for distance vision, because I mostly use that when I'm outside and I hate not being able to wear sunglasses because I seem to be sensitive to glare.

My optometrist suggested that I could also try contacts for close work and she could work out a prescription for sunglasses that could be worn as well, that corrected my distance vision. Unfortunately, it proved impossible to get a set of contacts that gave me good enough close vision, so I had to scrap that plan. Might be worth checking out, though.

I got a few prices from different spectacle places and you'd be amazed at how much the prices differ - best was $499 for the two pairs (Specsavers) and worst was $950. It pays to shop around. I'm not comfortable buying glasses on-line because I can't try them on - it's not just about the look, it's also about the way they feel on my face. An important consideration is where the lens sits relative to your eyes in terms of height - with modern small lenses, this is quite critical in making sure you can see through the glasses rather than looking around them. For example, my current glasses are rimless titanium ones, which minimise the visibility of the edges from my perspective, but the bottom edge of the lens is exactly where the edge of stairs are when I walk down them - I have to tilt my head down slightly to see the edge of the stairs.

a pair of single-vision glasses for closer work and a pair of prescription sunglasses for distance vision

I did this recently, getting a pair of distance-only glasses and a pair of reading/computer glasses to augment my no-line bifocals. I tried out zenni optical (frequently mentioned on metafilter) for this and was very happy with the results. They were cheap enough that I just decided to give it a try and toss them if they didn't work out. I'm actually much happier with them than I was with my previous $400 glasses from walmart. All 3 pairs were under $100 total.

I'm going through contact lens angst at the moment. I tried monthly torics (for astigmatism), and couldn't get along with them. This week I started a trial of daily disposable torics, which seem ok-ish, too soon to tell. But I suspect I'll end up with normal daily disposables and reading glasses, which I don't mind. I have a few pairs of reading specs, all cheap-ish ones, and they're fine.

My prescription glasses are varifocals, with the main prescription for myopia and astigmatism and a mild reading prescription added in. The lenses are always horribly expensive, due to the need to have high indexation lenses to avoid Coke-bottle specs. I've been going to the same opticians for 15 years and always see the same person. Although I could probably get a cheaper service from a chain, I like the consistency of seeing the same person every time.

Yep, go to the drugstore and try on different strengths, and choose whatever feels right. I got tired of how fast the really cheap ones would break; whenever I had a pair I thought looked good, they'd disintegrate. Found $7 readers on the web in a style that's pretty good, and they've lasted way longer. I have a cup-o-glasses in both bathrooms, and when I had to rip apart my room due to the flood a couple weeks ago, I found several pair.