All undergraduate applications are all lodged through UCAS, a centralised application system for undergraduate studies in the UK. In a nutshell, an applicant can choose up to 5 universities of his/her choice by only sending 1 application in UCAS.
The application is quite standard: personal details, education history, personal statement and recommendation. The last two components are the most crucial ones. In personal statement, the applicant writes the reason why he/she wants to study the chosen major, without stating any particular university (because the statement will be sent to 5 universities, you cannot mention any one of them in the statement). For reference, the applicant needs to assign one person to write the reference (typically, this would be his/her high school principal or teacher). The applicant would then write the refferal’s email and the system will email the referral asking him/her to write a reference for the applicant. Remember that it is your job to remind the referral about the deadline!
The deadline for UCAS application is January 15. After applying, you just need to wait until the university gives you a reply. For some schools and majors, additional tests, interviews or portfolio may be required. Do check!
Postgraduate applications are different across majors, schools and universities. Please check their respective websites for more details.