Verb + 着 (ongoing state)

The door is open

• You come home and notice the door open and the lights on.
• 门开mén kāi(ongoing)着zhe，lamp灯dēngalso也yěbright亮liàng(ongoing)着zhe。 — "The door is open, and the lights are on too." (ongoing)着zhe describes a state that continues.

Verb + (ongoing)着zhe = an ongoing state

• Verb + (ongoing)着zhe describes a state that lasts: to open (transitive or…开kāi(ongoing)着zhe (is open), attire穿着chuān zhe (is wearing), to sit坐zuò(ongoing)着zhe (is sitting).
• Negate with not / haven't没méi: gate门ménnot / haven't没méito open (transitive or…开kāi(ongoing)着zhe — "The door isn't open."

she她tāwear穿chuān(ongoing)着zhea一yí(measure word)件jiànred红hóngtop衣服yī fu。

Doing one thing while in a state

• Verb1 + (ongoing)着zhe + Verb2: the first state goes on while the second action happens: he他tāsmile笑xiào(ongoing)着zhesay说shuō："it doesn't matter没关系méi guān xi。" — "He said with a smile, 'It doesn't matter.'"
• we / us我们wǒ mento sit坐zuò(ongoing)着zheto chat聊天liáo tiān。 — "We sat and chatted."

he他tāsmile笑xiào(while)着zhesay说shuō：it doesn't matter没关系méi guān xi。

State, not progress

(ongoing)着zhe versus (in progress)在zài

• (in progress)在zài + Verb = in the middle of doing: he他tā(in progress)在zàiwear穿chuāntop衣服yī fu — "He's getting dressed."
• Verb + (ongoing)着zhe = the resulting state: he他tāattire穿着chuān zhea一yí(measure word)件jiàn白衬衫bái chèn shān — "He's wearing a white shirt."

he他tā(in progress)在zàiput on穿chuānclothes衣服yī fu。

Recap

Read the full reference: HSK 3 grammar — Particles.