You don't need a 1:1 teacher but I recommend starting with a community of sorts, with classes led by a teacher. Find a Buddhist prayer center. Don't worry if you don't believe in God or religious dogma; none of that's important with the communities you're trying to enter. (Buddhism is theologically agnostic, and although the religious believes in past lives, you won't be rejected by Buddhist communities if you don't believe in past lives or reincarnation.)

Once you've gained a sense of what approaches work for you, it's a good idea to get some books and study them. One great thing about zen/meditation books is that you can read them every year and they're still fresh-- there are things in them that you didn't pick up the last time because you weren't ready for them.

You can start practicing meditation using books. But joining a meditation group helps enormously.

While the instructions for meditation are truly simple, taming the mind is not :). There are some pitfalls we all walk into, like attachment to serenity that meditation can bring or getting discouraged by roadblocks. Having a teacher or joining a group helps you not getting stuck.

In cities, there are groups in different traditions (e.g. Vipassana, Zen, Diamond Way). These traditions have similar goals and methods, they can 'feel' very different. So, it's good to sit in with different groups once or twice to see where you feel at home.

With respect to books, I really enjoyed "Zen Mind, Beginner's Mind", but it can be a bit daunting. Philip Kapleau Roshi's "Three Pillars of Zen" is said to be a good introduction.

The OP article is as good exposition of Buddhist thought and practice as you will find. Shunryu Suzuki mentioned in it was an exponent of the Soto school of Zen which emphasizes 'just sitting'. Just that, sit with straight back. Look up 'seiza' for more information if you wish, but no need to get too technical. Also, I believe there are online meditation support groups if none are available near you.