The first difficulty that you're going to face is ensuring that you don't lose any of your design during the printing and cutting process of the card that you are designing. You also need to be aware that if your client is in another country, the size of their business cards may change. Once you know the size that you need, you need to make sure that you have a bleed that gives you room for the cutting and printing process.
A bleed simply allows a margin of error on the outside of your design.
Finish that, and then decide what orientation the card is going to be made. Vertically or horizontally. Last step in this process is to make sure that you have the proper resolution to create a sharp image when the printing process is complete. Setting your creation to about 300 DPI is ideal.
First step is to find a place for your client's logo. Remember that the logo is responsible for showing off the business. It should be in a place that's easy enough to see, and draws in anyone who sees it. There should be a one-line slogan or pitch involved as well. It needs to be quick and easy to read. It should be catchy, yet professional.
Then you have the obvious parts to complete the purpose of a business card. Contact information and a website or publicly available e-mail address.
Quick tip. Use a proper font. These cards aren't going out the children, generally. These cards are a professional miniature billboard. The font should be readable, and professional. No Comic Sans. No unreadable script.
Printing and the Final Steps
It doesn't matter if your design is amazing and perfect, and all your information fits beautifully. If you print it on low quality paper, whoever receives the card is going to think it came off of a home printer. Think of what fits the client's expectations, and adjust accordingly. Stay within budget, but don't pass up on quality. What kind of paper is up to you, check out the options at your print shop.