How do you go about pricing your services for profit?

Over time it's not uncommon to raise prices to match inflation. Good communication to clients will handle that.

For setting price points - Different industries have different profit margins. Setting the price is a tough one. You don't want to be too high or too low and obviously have a profit margin that is sustainable. The lowest hourly charge i've found sustainable in any business has been $60 per person. Other businesses have higher minimums. This is my personal experience. 
We personally priced our Dog Poo Pickup service to be the highest price in the market for the pay as you go packages. And the cheapest in the market if someone pre pays for a year of service. This way the subscriptions not cover more than the cost to run the business on a monthly basis and the prepaid funds just collect in the back. This means we will never be in a deficit unless I make dumb financial decisions lol. 

You want to get the knowledge of what it costs to run your business and break that down to an hourly cost. including all your expenses not just the cost to do the job. Then you will see the true picture of the cost to run your business and you can decide what you need to charge to be sustainable.

Depending on the service industry you're typically looking at a range of 10%-35% profit margin. Do your market research to see what other services are charging and you will get your ball park price and can strategize from there what you want to do. 

It's important to do an After Action Report- How do you know how much you need to charge if you don't know if the previous job was profitable? Reviewing each job, assessing it's worth in Time, Materials, and Labor may change your perspective on how much you should be charging. It may not be one or two jobs, but do the same project 3 times and see if it was really worth your while at that price point.