On which side of the bean/pea need the strings be removed? I have done this for years but I often get strings on both sides. I feel really dumb about this!

Unfortunately, it depends on what varieties you're growing. While I think that most pea varieties still require stringing, many modern snap-bean types are stringless.

I only grow stringless beans; it's too much work! But sugar snap peas are worth the trouble. They usually need stringing on both sides.

We (my family) have always broke beans ends and checked for strings on both sides. Even the "modern" stringless beans sometimes have strings. Hard to chew beans with strings attached..LOL. So better safe than to be pulling strings from your mouth while eating..LMFAO