I have worked for both small as well as large businesses, I have also freelanced and contracted. My advice is that you can start right now by paying careful attention to what you are working with (technology wise). There are specialists from various disciplines present in big organisations, but segregation of duties can be a ceiling on what you will be allowed to be and do:
Join as many developer networks as you can. Contribute as much as possible. Talk to people in your company. Make new connections. If you are certain of the area you would like to specialise in this will be easy. Else, the following points might help:
Choose. I know this sounds silly, but with divided attention makes it difficult to grow.
Study the technology you chose. You can learn by doing online tutorials or signing up for a course. Be diligent. It does pay off... find like-minded people to link up with to help get you through. We also learn by teaching others - start a blog or contribute to an open source project.
Finally, just enjoy it. The world of technology holds many opportunities for people who are willing to do what it takes. Have courage. Look after your health and emotional well-being. Stand out. Be strong