You can get the new crops from Leif's plant stall.
The five new crops added to the game are sugarcane, potatoes, tomatoes, carrots, and wheat, and the most reliable way to find them is to visit Leif. He'll have two different produce starts in his shop each day for you to choose from so you can slowly collect them all.
Leif will visit your island once a week, so you'll want to check his offerings when he comes to visit. If you're impatient and don't want to wait weeks to collect all of the new crops, you can also open his shop on Harv's Island.
Visit Harv's Island and speak to the different gyroids waiting to set up shop. You'll want to donate to the one accepting funds for a "botany expert with the greenest of thumbs" (if you couldn't already tell that one was Leif). It's 100,000 Bells to donate, but if you don't have enough Bells on your person when you arrive on the island, you can take some out using the kiosk next to the entrance of the plaza. Once you donate the full amount, Leif's shop will be available the next day.
Just remember, you can only open one new shop a day on Harv's Island, so you'll have to prioritize the shops you want first.
His produce offerings rotate, so while you can buy from him every day on Harv's Island (as opposed to once a week on yours), it may take a few visits before you manage to gather seedlings for all of the crops.
You can also find the new crops on Kapp'n's Mystery Island Tours.
If you're still having issues finding all of the new crops you need through Leif, luckily there is another way to find them — though it's not as reliable. Every day, you can go on one Mystery Island Tour with Kapp'n, where you pay 1,000 Nook Miles for him to take you to a new island that may (or may not) have rare or seasonal items on it.
There are a variety of different islands Kapp'n may take you to, and one of them is an island with the new crops on it.
Some players have gotten lucky and found an island with most of the crops they're missing on it, while others have only managed to find one new one at a time. Again, this isn't the most reliable method, but it is one way to get new crops.
You can harvest the crop on the mystery island to take home to cook with. Unfortunately, the new crops aren't like fruits in that you can plant to grow a new crop — though some plants can be dug up and brought home with you.