Design has always been a huge part of my life. I love everything to do with art and design. Inspiration does not have a schedule. It can hit you at any time and place; this is why I bought myself an iPad. As a person who does design the iPad is not the best out there - Microsoft Surface is quite the competition here. Apple is still taking its sweet time in opening the system and giving it the chance to grow up, but until Apple does that the iPad can still do a lot if you know what you are doing.
I have tried many applications, and there are many out there competing for your attention. The ones that caught my eye are two:
I love this app. It is simple and you can do a lot with it. The app is free filled with basic shapes and fonts. You can go for a monthly subscription for about $10. The subscription comes with many bells and whistles to help you with your design endeavors.
What I love the most with this app is having unsplash.com whole high-quality photo archive for users to use in designing pictures for their websites.
Another little trick this app does that I love is having presets. The app presets are ready to go if you're planning on moving your logo design to your Facebook page, Twitter, or Google Plus.
2. Graphic by Autodesk
This is my second app that I use extensively to design everything from posters, to business cards, to company and business logos. Graphic is a bit more technical but users should be able to get the hang of it pretty quickly. There are tons of videos on YouTube to get you up and running in no time.
The picture below is my business card.
If you're inexpereinced I would say start with Over.