• Basic forms
• 泣く — to cry; to weep / base form
• 泣きます — cry; weep / masu form
• 泣いた — cried; wept / ta form
• 泣いて — crying; cry and … / te-form
• 泣かない — do not cry / negative form
• 泣けば — if (someone) cries / conditional
• 泣け・泣きなさい — cry! / imperative
• Other common forms
• 泣きたい — want to cry / 〜たい form
• 泣ける — can cry; be moved to tears / potential
• 泣けた — was able to cry / past potential
• 泣けない — cannot cry / negative potential
• More
• 泣こう — let’s cry / 〜よう form
• 泣かなかった — didn’t cry / past negative
• 泣いている — is crying / progressive

泣く（なく） is a godan verb ending in く. The stem alternates as く → き → い → っ, as seen in 泣く・泣きます・泣いて・泣いた. Used specifically for people crying; for animals or sounds, 鳴く is used instead.