我紧张。

You can use it as a standalone sentence. Just say 我紧张 when someone asks how you feel. To make it stronger, add 很 (hěn) to say 我很紧张. It works just like an adjective in English. You do not need the word 'am' (shì) here. Just subject plus the feeling.

Use it before a big presentation at work. Use it when you are about to ask someone out. It is perfect for when you are waiting for exam results. If you are stuck in traffic and late, you might feel 紧张 too. It is great for sharing your internal state with friends.

Do not use it to mean you are 'scared' of a ghost or a spider. For that, use 我 afraid (我怕). Also, do not use it to describe a 'busy' schedule. While 紧张 can mean a tight schedule, people usually say 时间很紧. Avoid using it if you are just angry or annoyed. It is specifically about that 'on edge' feeling.

In Chinese culture, admitting you are 紧张 is often seen as being humble. It shows you care about the outcome of what you are doing. It is a very 'human' expression. Friends will usually respond with 别紧张 (don't be nervous). This is the standard way to offer comfort and support.

You will often hear 别紧张 (bié jǐnzhāng) which means 'don't be nervous.' Another one is 有点紧张 (yǒudiǎn jǐnzhāng) for 'a little nervous.' If you are extremely nervous, you can say 紧张死了 (jǐnzhāng sǐ le). This literally means 'nervous to death.' It adds a bit of dramatic flair to your day.