If you are going to ask your Boss (which is the correct way to do it) - the first thing you need to do is coach it from your Boss's perspective.
What do I mean by this?
You want to make a business case to your Boss and the wider company as to why it is in their best interests to pay you more:
- The Value you bring to the Company (even better if you can give them a Dollar figure), note this can be either Revenue grown or costs decreased
- The recent tasks/projects you have successfully completed
- If the company has been doing well (increased sales)
- Inflation costs
- The cost to replace you (at minimum, a new hire is going to take 3-6 months from initial hire to become truly productive)
- What the current market rate for your position is.
You also want to give a figure, I always suggest between 5-10% higher than what you would actually accept - so that if there is any rounds of negotiation, you can come down to what you actually want.
If this isn't successful, then absolutely that is the right time to start looking elsewhere. One thing to note - if you ask for a Raise, they decline, you then hand in a resignation offer and they then magically find the budget for a Raise - my best advice would be to not accept it - if they weren't willing to pay you what you are worth when they didn't think you were leaving, why would they be willing in the future when they know you are looking elsewhere?