I can't find these anywhere. Could somebody please simplify the differences between class 1-5 for newbies like me.

If you are interested in mountaineering pick up and read a copy of "Freedom of the Hills" as a primer.
1 - Hiking trail
2 - Off trail, scree slope, occasional use of hands.
3 - Frequent use of hands, steep enough you need to face the slope to down climb.
4 - Steep class 3 with exposure but easy handholds - but if you fall you could die.
5 - Technical climbing - need a belay.

To clarify, we're talking now about the Yosemite Decimal System, which isn't used very much outside the United States.

Within the US, it's used almost exclusively by rock climbers, and almost exclusively for ratings of 5.5 and up. For those, there's usually a decent consensus on what a given route should be rated. For the lower ratings, people generally don't know (or care) where to draw the lines between classes.

Here's what the 7th edition of FOTH says:

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1. Hiking
2. Simple scrambling, with possible occasional use of the hands.
3. Scrambling; a rope might be carried.
4. Simple climbing, often with exposure. A rope is often used. A fall on Class 4 rock could be fatal. Typically, natural protection can be easily found.
5. Where rock climbing begins in earnest. Climbing involves the use of a rope, belaying, and protection (natural or artificial) to protect the leader from a long fall.
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Same basic hierarchy as what Bark Eater said, but different criteria: no mention of trails, or down-climbing, or facing in or out...

I personally like the "number of limbs" approximation:

class 1: Smooth enough that a determined person could navigate it by hopping, or with a pogo stick. You can imagine a really good unicyclist might give it a try.
class 2: still basically walking. A really good mountain bicyclist might try it, at least for descent.
class 3: two legs plus a hand. Hand is primarily for balance.
class 4: All four limbs needed.
Class 5: All four limbs plus a rope.

So an amateur could do class 2, maybe class 3?

Yes, anybody can do class 3 unless they've got some kind of major physical impairment. If you've got an appetite for risk, you could handle class 4, the basic definition of which is, it doesn't require any more technique than you'd need for climbing a ladder. The problem is, it's not always easy to tell from below whether a route is going to be class 3 or class 4 or class 5, so a good rule for beginners (and unroped climbing in general) is don't go up something unless you're sure you can go down the same way.

Note also that an easy route is not always a safe one. There are plenty of class 3 routes where you could trigger a rockslide or an avalanche, slip and take a tumble over a cliff, get hit by falling rocks, etc. etc.

I've taken plenty of people rock-climbing for the first time, and it's not unusual for somebody to complete a short 5.6 or 5.7 route on their first day. (At 5.8 or so things get more physically demanding (and/or you have to have some technique to compensate), but somebody with, say, a gymnastics background can get there with hardly any practice. By 5.10 you're usually looking at a lot of practice and training.) The main obstacle to climbing mid-5th class for beginners is not usually the climbing itself, it's learning proper use of the rope and equipment. Then, doing it in the mountains involves a certain mental toughness, plus the physical strength to carry all that rope...

Class 1: Trail or easy cross-country hiking.

Class 2: This often translates into talus. Skip ahead to Class 3!

Class 3: I'm using my hands. This is fun. Who in the world would rope up for this?

Class 4: Why the hell didn't I rope up?

Class 5: Nartreb sums it up pretty well.

It also depends where you live. Class 3 in California becomes class 4-5 in Colorado.

So far, I think these are all pretty spot on. I like to use the 'relative' YDS scale:

Class 1: I would take my toddler on this as his/her first hike
Class 2: I would take my aging parents on this.
Class 3: I would take my wife on this, carrying a rope, just in case, especially for the descent.
Class 4: I would take my wife on this, but belay her on all of the class 4 sections. We would also rappel or belay down climb.
Class 5: I would not take my wife on this, but my climbing partners and we would rope up and belay each pitch.

Class 1: Easier than class 2 but harder than hanging out in the mall.
Class 2: Harder than class 1 but easier than class 3.
Class 3: Harder than class 2 or 1 but no harder than class 4 and usually easier than class 5.
Class 4: Harder or maybe just more dangerous than class 3 unless you're in Colorado but easier than class 5 except when class 5 is actually easier.
Class 5: Harder than class 3, usually.

In WY it's either
1-5 in summer: Yer fine.
1-5 in winter: Yer fine.
1-5 in grizzly country: Flip a quarter!

One analogy I learned is to pretend you're holding a mug of really hot coffee.

Class 1: You can do it while drinking your coffee, and you won't spill it.
Class 2: You wouldn't want to drink your coffee while doing Class 2, but you'd hold it without a lid.
Class 3: You should probably put a lid on your coffee on Class 3, or clip it to a harness.
Class 4: You should probably put your coffee down, and ask a friend to spot you.
Class 5: That coffee should be put away, and you should be protected with a rope.