There are two different questions hiding inside "how do I get found on Google", and they have different answers. The first is being found when somebody searches your business name. That is nearly automatic and happens within days of going live. The second is being found when somebody searches for what you do, like plumber in Tauranga, and that is a real competition against every other plumber in Tauranga.
For the first, you need a live site with your business name on it and a bit of patience. We write your sitemap and your robots file automatically and point Google at them, so there is nothing for you to do.
For the second, the thing that matters most for a local business is not on your website at all. It is your Google Business Profile, which is free, takes twenty minutes, and is what fills the map box at the top of local results. A business with a complete profile and a handful of reviews will usually beat a business with a better website and no profile.
After that, the highest-value thing on your own site is saying plainly what you do and where you do it, in your own words, on more than one page. Not stuffed with keywords, which Google has been able to spot for twenty years. Written the way you would say it to a customer standing in front of you.
How long it takes. Days to weeks to be found for your own business name. Months for competitive phrases like "plumber Tauranga". Anybody promising faster is guessing, and anybody charging you monthly to promise it should be asked exactly what they will do.
Step by step
Make sure every page has a clear heading saying what it is.
"Plumber in Tauranga" beats "Welcome" by a distance.
Put your town in your words on more than one page.
Fill in the page description in the SEO tab. That is the grey text people read in Google results.
Set up a free Google Business Profile.
For a local business this is often worth more than everything else on this list put together.
Put your address and phone number on your contact page as real text, not inside a picture.
Ask a few happy customers for a Google review.
If it does not go to plan
Do I need to submit my site to Google?
Not really, but it speeds things up. Set up Google Search Console, which is free, and use URL Inspection to ask for a page to be looked at.
Should I pay for ads?
Not to be found for your own name. For competitive phrases it is often the only fast way, but do the free things first or you will pay for traffic that lands on a page that is not ready.
Someone is offering me SEO for $300 a month.
Ask exactly what they will do each month, and what they did last month. A good answer is specific. A bad one talks about rankings without naming a single action.