Read the book "Financial Intelligence for Entrepreneurs" by Karen Berman & Joe Knight. Even if you'll have somebody else doing your accounting, you'll still need know what those numbers mean and how to do some financial analysis. This is the best book I've read that talks about these issues with respect to the entrepreneur.
So you are aware finance can mean several different things.
Accounting in my mind is the language of business and I agree with Stefanos Tses answer on talking to your accountant on serious issues but to make even day to day decisions on the business requires some understanding of accounting. I'd suggest querying on income statement, cash flow statement and balance sheet. From a pragmatic position understanding basic budgetting and profit analysis can get you started so you have a tool set for making decisions. I believe the understanding of accounting is important enough that I would suggest taking a class on it while you are going after your business. After a class on the basics you will have the tools to make the day to day decions or at least have a frame work for how to make the decisions.
Another book in that subject matter is Small Business for Dummies. It's not too sexy, but it will get you the basics on what's involved in running a business. Even just a general book on accounting can get you started. Our local community college has an entrepreneurship class that covers small business accounting and tax matters, as well as several other topics. That could be another avenue to expand your knowledge.
I would go and do a relevant short course on finance.
When I first started, I knew nothing about finance. Doing a course was great for me because I had to learn to construct financial statements and do financial modelling. Now I am quite good at finance but I would never have got those skills from reading a book.
The only proviso I would give is try to find a course on entrepreneurial finance rather than straight accounting as the approach is slightly different.
Another good way to practice is to always do the numbers for any idea you think of. It conditions you to think about business from an income/expense/profit perspective!