You must apply for university through UCAS (the Universities and Colleges Admissions Service). For most undergraduate courses, the deadline is in January of the year when you want to go to university. However, some deadlines are the year before, in October (especially music courses, and courses at Oxford and Cambridge), so make sure you check.
Most full-time Bachelor degree courses are 3 years long in England and Wales. In Scotland, they are usually 4 years.
In Scotland, university is free for many people, including most school leavers.
In England & Wales, adult learners might be able to get a grant or bursary.