I got into scuba diving through lessons at a community college; it was very inexpensive. You will need to provide mask, snorkle, and fins at a minimum; you don't have to get top of the line stuff and could even buy used. Just make sure the items fit properly and are reasonably comfortable. Total investment in gear less than $100 normally, maybe $150 or so if you go for name-brand items. An open-water scuba certification course will probably be $150 to $300, perhaps a bit more if they are doing boat dives.
First, you have the cost of getting certified. Prices for the course and pool work portion of your scuba diving certification can range anywhere from around $150 to several hundred. I think $200-$250 is probably about average for the course and pool portion.
If you take the book portion online through PADI, the course currently costs $120. You still have to pay for your in water training and open water dive portions of the course.
The price of your open water certification dives vary depending on where you take them. For instance, looking on the internet, an operator in Grand Cayman charges $325 for the 4 certification dives. The dive shop I used while on my last Cozumel scuba diving vacation was charging $185 for the 4 certification dives. So scuba diving prices can vary fairly widely depending on where you go. Estimate about $200-$250 or so on average.
So figuring in the cost of your book, pool and open water certification dives, total cost of scuba diving certification will probably be about $350-$450. Using the same two operators I mentioned
above as an example, the total cost of certification (book, pool, open water) through them would be $500 and $368.
Adding to your scuba cost is the the fact that you will probably want to get (or will be required by your course instructor) to get your own mask, fins and snorkel (as I discuss here.) There is a wide amount of leeway here but figure about $150-$200.
If you want to get a full set of good quality gear (the above plus BC, computer and regulator), that can easily run you over $1,000.
Then you can get into buying all other sorts of accessories such as wetsuits, watches, dive bags, etc. You can spend as much or as little as you want on these other items. Whatever works for your wallet.
If you are diving with a dive shop, the most common dives are 2 tank boat dives. As with the certification dives, the cost of your dives varies depending on the island and the operator. As a ballpark, in the Caribbean you can expect to pay anywhere between $75-$100 for a 2 tank boat dive with closer to $75 more the norm.
However, on our last dive trip (to Cozumel) we paid $58 for a 2 tank boat dive so it was relatively cheap. This also included our BC rental since we didn't bring our BC's on that trip.
If you want to rent your gear (BC, regulator, computer) a set of rental gear for the day will be in the ballpark of $25-$50. Some operators include it in the price (not the norm) and some have a discounted price for week rentals.