Wood furniture refinishing tips?

My husband and I are still using the dresser and chest that were mine when I was a little girl. They are good, sturdy wood. I hate the idea of getting rid of them when it’s still a great functioning piece, but they definitly need a makeover.

They seem to be finished with veneer. I want to strip that, sand it down and re-stain it (I LOVE the look of wood and would prefer to not paint these pieces).

I’ve been watching a lot of FB videos and reading some Pinterest blogs.

But I was hoping to hear from anyone first hand, what refinishing methods they recommend?

A wet towel, iron and scraping seems to be the most common way to get it off.

After the veneer is off do you sand it, touch up holes, condition and then stain it?

All tips and advice greatly appreciated! :)