These skills will be the same whatever business you run - whether you're a sole-trading graphic designer or you head a manufacturing company employing dozens of people.
There are intangible skills you will need, such as leadership skills, the ability to cope with long hours and hard work, and the inner resources to deal with stress and risk-taking. They also include strategy-setting and the ability to build and manage a team.
There are also functional skills that all businesses need. The smaller your business, the more of these skills you will need personally:
Finance - including cashflow planning, credit management and managing relationships with your bank and accountant
Marketing - including advertising, promotion and public relations
Sales - including pricing, negotiating, customer service and tracking competitors
Procurement and buying - including tendering, managing contracts, stock control and inventory planning
Administration - including bookkeeping, billing, accounts preparation and payroll handling
Personnel - including recruitment, dispute resolution, motivating staff and managing training
Personal business skills - including computer, written and oral communication, and organisational skills
As a business owner or director you also need the skill to know when it's best to hand over tasks to others by delegating, recruiting and outsourcing.