Self-promotion and how to market your brand to potential clients

Only one column this week (because, sigh, #reallife), but we're tackling two questions from readers today that cover some similar ground!

Here's the first question, from I.M.:

I'm a 24 year old designer with 5 years of actual work experience. I'm entering that stage where I'd like to start finding my own personal clients for my side gig and I'm finding it difficult. I'd like pointers on how to put myself out there (apart from the web) and how to approach people whom I think I can help. I've seen so many cute local businesses popping up where I'm from (Puerto Rico) and I'd love to be able to offer some of these businesses my expertise!

And here's another variation, from T.F.:

How do you promote and sell your brand and products to potential clients?