Increase in an asset, decrease in another asset

How to determine to increase or decrease in accounting

You're asking two different questions. As to the first one, issuing stock for cash is an increase in the cash (asset) and an increase in the stock (equity). Stock IS NOT an asset. The company doesn't own it, nor have any claim on it. The stockholder is the one who has the claim, so it's equity.

As for the second question, it's ambiguous. You have to understand the transaction and determine what it means, which accounts are to be used, whether you're increasing or decreasing them, what classification of account they are... and if you're into debits & credits (which you haven't said), then which rule it will follow. That's an entire chapter's worth just to get started and requires practice and experience. So it's a very broad topic that no one can answer in some simple manner.

If you're stuck on something specific, you'll have to ask a specific question. (Do keep in mind that we don't just do homework for people, so either supply your attempts at the problems, or just ask a question about a concept you don't understand.)