ましだless bad; at least …
まし is "less bad": better, but only among things that aren't good. With it you pick the lesser evil, settle for better than nothing, or find the one saving grace in a bad situation: "at least …".
the lesser evil
Taking the long way around on foot is better than waiting here for two hours.
better than nothing
Even bland emergency food is better than eating nothing.
at least
It is quite cold today, but at least it is not raining.
The lesser evil
A より B のほうがましだ
より follows the worse one. A verb takes ほうが without の, in the dictionary form or the た-form: 歩くほうがましだ, やめたほうがましだ.
Better than …
A より（は）ましだ
Without ほうが, when it is already clear what you are judging. ないよりましだ is "better than nothing".
At least …
Plain form + だけましだ
A な-adjective keeps な: 静かなだけましだ. A noun takes である in writing and な in conversation: 個室であるだけましだ, 個室なだけましだ ("at least it's a private room").
Less bad, not good
English "better" can be praise. まし isn't: it says neither thing is good, and this one is the less bad. People say it with a shrug, mostly in conversation. Said about a present, or about work someone has done, it is rude.
This report is better than your last one.
Praise.
This report isn't as bad as your last one.
Both were poor. This one is only less poor.
The lesser evil: より・ほうがましだ
A slightly heavy umbrella is still better than one that is falling apart.
I'd rather be a day late and apologize than stay up all night to finish it.
The pain is still there, but it is better than yesterday.
It's a small umbrella, but it's better than nothing.
At least: だけましだ
First the bad news, then the one thing that keeps it from being worse. だけ here isn't "only". It is "by that much": things are better by that one fact.
The pay is low, but at least there is no overtime.
The train was delayed, but at least it was not canceled.
This hotel has old facilities, but at least it is quiet.
About your own troubles, it is making the best of things. To someone else about theirs, it can come out as "stop complaining".
At least you have a job.
To a friend who is grumbling about work: comfort or a telling-off, depending on the voice.
Three more you'll hear
まだましnot so bad, by comparison
Today's heat isn't so bad compared with yesterday's.
もっとましなa better, a more decent
Can't you come up with a better excuse?
ましになるget a bit better; not as bad as it was
I tidied up, and the room isn't quite so bad now.
Close neighbours
くらいならN3
Throws one choice out and names what you would do instead. The sentence often ends in ほうがましだ.
I'd rather die than apologize to that person.
より・のほうがN5
The plain "better", "cheaper", "faster". Nothing is wrong with the one that loses.
This shop is cheaper than the shop by the station.
Check yourself
1A friend has given you a scarf, and you like it more than your old one. Which do you say?
Choose an answer to see why.
2What does this person think of the restaurant?
この
Choose an answer to see why.
More sentences
Even an awkward apology is better than saying nothing.
Explaining it yourself, even at the risk of embarrassment, is better than staying silent and being misunderstood.
The two halves can swap. より still follows the worse one.
If the noise is only this bad, it is still better than my previous room.
The seat is right at the back, but at least I can sit down.
I was injured, but at least I did not break any bones.
The power is still out, but at least we have running water.
The room is small, but at least it is a private one.
A noun, with である. Said aloud it is 個室なだけましだ.