• Basic forms
• 好む — to like; to prefer / base form
• 好みます — (I) like; prefer / masu form
• 好んだ — liked; preferred / ta form
• 好んで — liking; willingly / te-form
• 好まない — do not like / negative
• 好めば — if (someone) likes / conditional
• 好め — like it! (rare) / imperative
• Other common forms
• 静かな場所を好む — prefer quiet places
• 好みたい — want to like / 〜たい
• 好める — can like; be inclined to like / potential
• More
• 好もう — let’s like; let’s choose / 〜よう
• 好まなかった — didn’t like

好む（このむ） is a godan verb ending in む. Common and neutral — used for preferences, tastes, and tendencies.

• Basic forms
• 好く — to like (literary / fixed usage) / base form
• 好きます — likes / masu form
• 好いた — liked / ta form
• 好いて — liking / te-form
• 好かない — do not like / negative
• Common expressions
• 酒を好く — to like alcohol
• 人を好く — to be fond of people
• More
• 好こう — let’s like (rare)

好く（すく） is a godan verb, but its usage is limited. Mostly seen in literary style or fixed expressions; 好む is preferred in modern usage.