Quell your capriciousness. Rely less on mere desire and intuition and more on facts, details and logic when making decisions, big or small. Practice perceiving not only how appealing a certain course of action is, but on the many possible outcomes and alternatives to options you're considering or problems you're considering.
Think before you speak. Make a habit of using conversational silence to consider your words carefully rather than immediately and abruptly responding as soon as another person stops talking.
Force yourself to read instructions, rather than dig into an assignment, project or product assembly determined to figure everything out as you go.
Make plans, and stick to them. Contemplate the long run, and map out a five- or ten-year plan for your life. For the short run, make weekly schedules and daily to-do lists to keep yourself organized and feel more accountable for your goals.
Spend time partaking in complex activities or hobbies requiring intense logic and strategy, such as playing chess or solving brainteasers.
Dedicate more time to reading challenging books and publications that make use of sophisticated expression and complex vocabulary. Focus more on details as you read. Don't just read the words of a poem or within the pages of a book - read between the lines. Think about why a writer has chosen one word over another, or has included specific descriptions at all.
Build your written communication skills. Right-brained individuals tend to have more trouble expressing themselves in words than do left-brained people, so give writing tasks the extra time that they require. Consider keeping a journal to make regular practice of writing effectively. Force yourself to proofread for spelling and grammatical accuracy whether writing for yourself or others.
Stop fleeing from numbers, and embrace them. Complete your own taxes, manage your own accounts, develop your own budget, determine your own share of the bill and calculate your own change. Attempt mental math first, before reaching for the nearest calculator. If you're really serious about tapping more into your left brain, consider taking an algebra course as a refresher. Because algebra involves symbols reminiscent of grammatical writing, practicing and making use of that branch of math engages the left side of the brain more than other types of math.