There are a few verbs that will indicate that the following word is in instrumental case. Do you know what those verbs are?
There is a lot of such verbs. Technically if you can remake sentence with using by + participle or just using participle, or you can say that some action was made with, via or by way of something as an instrument it may be instrumental case.
Я написал письмо пером. ['ʝа nɐpʲɪ'sɑɫ pʲɪsʲ'mo pʲɪ'rom]
I wrote (the) letter with (a) quill pen.
I wrote (the) letter by (using) (a) quill pen.
Говорит она сама с собою. [gɐvɐ'rʲit ɐ'nа sɐ'ma sɐ'boju]
She speaks to (with) herself.
Они решили перейти реку бродом. [ɐ'nʲi rʲɪ'ʂɨlʲɪ pʲɪrʲɪj'tʲi 'rʲeku 'brodɐm]
They decided to cross the river via wade.
Mostly I agree with Stepan, but not fully.
Actually in Russian we have no instrumental case. We have "творительный падеж" or ablativ. It has function of instrumental case, examples of which you see in Stepan's answer, but it has also 12 more functions. You can find full list of them in Russian wiki.
One of the most interesting function of Russian ablativ is pointing to time or place. Check out these examples:
1. Я иду дорогой 2. Под мостом 3. Тем временем 4. Утром