How can I decorate my kitchen with farmhouse greenery?

Is this real greenery or silk flowers?

If silk or plastic, I would keep it away from the stove, as grease-laden vapors will make it trap dust & be a maintenance hassle down the road.

For now, I would use very fine nails, called “brads” and very fine wire and twist tie it to the nails, which would be tacked-in at an angle.

although I break my own advice (I do have artificial greenery over a bookcase) I would not decorate with artificial flowers, even silk ones. Use really ivy.

I had a long garland of artificial ivy for years above my cupboards. I would soak them in a soapy mixture in my bath tub (Dawn dish detergent or cheap shampoo) whenever they got greasy and/or dusty. Then I would drip it dry over the tub after rinsing or hang up outside. It was a bit of work, but, as I said, I kept it for years, and loved the look.