The best way to land a client, and the only way I've found so far, is to implore those who love you to give you a chance. Family members, friends, friends of your family. Start with anyone who has a positive opinion of or an emotional attachment to you. If they want what's best for you, and you can convince them that hiring you is what's best, they'll be more inclined to give you a chance.
I started by offering to do some work for free, although everyone says not to do this. I rewrote my cousin's website to give it a more polished feel. All I asked for was good reviews and to recommend my work in the future.
He didn't use my changes and didn't mention it again for months. Honestly I thought I must have ruined my chances. However, a few months later he contacted me to rewrite some blog posts for his website. Although he wasn't able to use the first project I worked on, he saw that I actually can write and he remembered that when he needed help with his blog.
Just keep begging for people to let you write for them. Eventually they'll give in. They always do.
Me talking about my skills at every family party.