• Basic forms
• 触れる — touch; come into contact / base form
• 触れます — touches; comes into contact / masu form
• 触れた — touched; came into contact / ta form
• 触れて — touching … / te form
• 触れない — do not touch / negative
• 触れれば — if (one) touches / conditional
• Common expressions
• 指が壁に触れる — one’s finger touches the wall
• 問題に触れない — don't touch on an issue
• 逆鱗に触れた — touched a raw nerve; incurred great anger

触れる（ふれる） is an ichidan intransitive verb. It often implies light or indirect contact, and is also used figuratively for mentioning topics briefly.

• Basic forms
• 触る — touch; handle / base form
• 触ります — touches; handles / masu form
• 触った — touched; handled / ta form
• 触って — touching … / te form
• 触らない — do not touch / negative
• 触れば — if (one) touches / conditional
• Common expressions
• 危ないから触るな — don’t touch, it’s dangerous
• 展示品に実際に触れました — could actually touch an exhibit

触る（さわる） is a godan transitive verb. It refers to direct, intentional touching or handling of objects.