Growing a Windowsill Garden

MM All-

I have lived most of my adult life in houses with yards and gardens and always had room for 'just one more plant or tree'.

For this past year I have lived in an apartment. I have a miniscule balcony I share with the apartment next to me. My growing takes place inside. I haven't had issues with the houseplants but for the life of me I can't get herbs to grow. Where they would grow in barrels and raised beds outdoors and flourish they simply will not grow indoors for me.

What am I doing wrong? Any tips?