Comparing things with より and の方が

より is used to compare two things in a direct way, like the "than" in "I'm smarter than you". When you use より, you do not need to use a "more" word, unlike English which needs to say "more X than Y" or "Xer than Y". Sometimes より can be followed by も for emphasis.

彼は誰よりも強いよ
He is stronger than anyone

In this given example, 誰より without も can come across as weird and is less common.

より is also used in constructions about relative position (in space or time), similar to から.

南より迫る
To approach from the south

新世界より
From the New World

This usage of より is common in written letters, where より marks the sender and へ the recipient.

If you want to list both sides of a comparison, you mark the lower bound with より and the upper bound with 方. 方 is a noun that reads ほう (don't be tricked by the かた reading!), and as per every noun, it attaches to other nouns with の and can take particles after it. In case of a comparison, the 方 "side" is usually marked by が whether or not it is the subject of the action.

メリットよりもデメリットの方が大きい
The cons are bigger than the pros.

The より side can be dropped if implied.

私は一人で行動する方が性に合っている。
It is more natural for me to act on my own.

Literally, this 方 usage marks a "side" of the comparison. XよりYの方がZ can be understood as "starting from the X side, the Y side is more Z" where X is the lower bound and Y the upper.

There are a few idiomatic expressions that make use of 方が.

<verb>方がいい means "it is better to do <verb>". It is common in this construction to use the verb in past tense if the statement comes from a position of personal advice rather than a general truth.

やめた方がいいと思います
I think it'd be better for you to stop.

少し余裕がある方がいいだろう。
It's better to have a bit of extra leeway I guess.

When いい is conjugated in past tense like 方がよかった it implies some regret or reprimand about an action that should or shouldn't have been done in the past.

真面目に戦った方がよかったのだろうか。
Would it have been better if I had fought seriously?