Learn Russian: Раньше я много спорил, а теперь решаю проблемы по-хорошему. - Earlier I argued a lot, but now I solve problems amicably.

It is formed from the adjective хороший (good) using the prefix по- and the dative ending -ему. While the adjective just means good, the adverb по-хорошему specifically means doing something in a good, peaceful, or amicable way, often to avoid a fight.

If по-хорошему means the nice way, how would I say the hard way?

You would use the exact opposite: по-плохому. In Russian, giving someone the choice between doing something по-хорошему or по-плохому is a very common phrase used to mean we can do this the easy way or the hard way.

Why does this sentence use а instead of но to say but?

The conjunction а is used to show contrast or comparison, especially between two different states, subjects, or times. Here, it beautifully contrasts the past (раньше) with the present (теперь). The word но is used for a direct contradiction or an unexpected result, which does not fit this comparison.

Why is the imperfective verb спорил used here instead of a perfective equivalent?

The word много (a lot) combined with раньше (earlier) shows that the arguing was a repeated, habitual action in the past. Repeated or ongoing actions always require the imperfective aspect.