If you're really serious about your career path I'd suggest a few things.
1- Being a lead designer is a coveted position, one that takes years to attain. That being said, it IS attainable but like yaustar mentioned, you're going to have to work your way up through the ranks. Some designers get lucky and score an entry design position right off the bat, while others start as game testers.
2- Start designing now. There are several games with free editors, which will allow you to create levels, mods or games of your own. You'll need the experience of designing games of your own and a solid portfolio if you want to get a job designing games professionally. Find a team of people that want to create a new game/mod or do so on your own, but start designing today.
3- Go to company websites and read their 'design' position descriptions. The job postings will give you an idea of qualifications they'll be expecting from you. Work towards those qualifications.
4- It's unfortunate but ideas alone won't get you a job, a track record completed designs will. Everyone who loves games has a game idea, it's the people who are willing to work hard and continue learning that score the jobs. Passion is a given in the game industry.
5- About schools. It's also important to remember that a college degree in game design doesn't guarantee you a job. Your work and dedication to being a designer will. Keep at it and work towards your dream!