The first time I restrung a guitar, I did it wrong in about four different ways and didn't even realize it until the strings kept slipping out of tune two days later. Nobody tells you the small stuff, they just assume you'll figure it out, so here's the version I wish somebody had actually walked me through.
Doesn't matter if it's your kid's first guitar or your own, the process breaks down the same way. What changes between acoustic, electric, and classical is really just how the string attaches at the bridge end. Everything else is close enough to identical that once you've done one, you can do all three.
What you actually need
A string winder helps a lot and costs almost nothing, but you can do this without one, it just takes longer. Wire cutters, for trimming the extra string once it's on. And obviously the new strings, matched to your guitar type. A guitar tuner too, whether it's a clip-on, an app, or a pedal, doesn't matter which.
One thing worth saying up front: change one string at a time, not all six at once. Leaving the others tensioned keeps the neck from shifting while you work, and it means you've always got a reference to see how the new string should sit.
Getting the old string off
Loosen the string first before you cut it. Turn the tuning peg until there's slack, then snip it somewhere in the middle. Trying to cut a fully tensioned string is more effort than it needs to be and honestly a little riskier for your fingers than people think.
On an acoustic, once the string's loose you'll need to pull the bridge pin out to free the end. They can be stubborn. A string winder usually has a little notch built in for exactly this, or a pair of pliers works if you're gentle about it.
On an electric or classical, once it's loose you just pull the string through, no bridge pin involved.
Acoustic guitars
The string end has a little brass ring on it, and that ring sits under the bridge pin, wedged against the underside of the guitar's top. Feed the string in through the hole, ball end first, then set the pin back in on top of it, slot facing forward toward the neck. Give the string a gentle tug while you push the pin in, so the ball seats properly against the pin instead of just floating loose in the hole. If it's not seated right you'll know almost immediately, because the string will pop back out the second you start tuning up.
Electric guitars
Depends some on the bridge style. Most common is a string that just feeds through the back of the body or through the bridge itself and out the front, no ball-seating step needed like acoustic. Pull it through until there's just a couple inches of slack at the tuning peg end, that's usually enough to wind properly without excess.
If your electric has a locking tremolo system (a lot of the higher-end ones do), that's a different process entirely with a locking nut and fine tuners, and honestly that one's worth looking up specifically for your exact bridge, because getting it wrong can mean the guitar won't hold tune at all.
Classical guitars
No ball end on the string, no bridge pin either. You're tying the string directly to the bridge. Feed the end through the hole in the bridge, then loop it back over itself and under, two or three times, and pull it snug so it locks itself in place through friction. It looks a little fiddly the first time but it holds fine once it's done right, and it's genuinely just a small knot once you've done it once.
Getting it up to pitch
However you got the string attached at the bridge, the tuning peg end works the same across all three types. Feed the string through the hole in the peg, leave a bit of slack, and start winding. You want the string to wind down toward the headstock as you turn, not stack up and away from it, that keeps the string angle over the nut cleaner and helps it stay in tune.
Bring it up to pitch slowly, checking your tuner as you go. New strings stretch, so it's normal for it to go flat again within a few minutes. Give it a gentle tug along its length once it's roughly in tune, retune, repeat that a couple times. That's basically how you skip the annoying "why does it keep going out of tune" phase that catches everybody the first few times they do this.
Trim the extra string once everything's holding steady. Leave a little bit sticking out rather than cutting flush, close enough is fine.
The part that actually matters
The mechanics of it are honestly the easy part. The thing that trips people up is patience, mostly. Rushing the tuning-up step, or not giving the string time to stretch and settle, is what causes the "I just did this and it's already out of tune" problem, way more than doing the bridge end wrong.
Riley's drum kit doesn't care about any of this, which she reminds us of constantly, but every guitar in this house has had strings replaced by hand more times than I can count at this point, so if it feels clumsy the first time, it's supposed to.
If you're not sure which strings actually fit your guitar, or something about your bridge doesn't match what's described here, that's exactly the kind of question we're happy to help sort out. No pitch attached, just don't want anyone forcing a string that doesn't belong.