You register as a private candidate and is allotted new roll no. And centre near your residence.you need not appear for all the subjects for improvement. Practical marks are carried forward as it is. the improvement exam mark sheet is same as your initial marksheet except instead of passed a line mentioning that its your improved result is written.however it doesn't matter. All colleges accept the score, all companies do, you just need to produce both the marksheets wherever you go.

I'm considering you as a cbse student so you'll considered as a private candidate in cbse  improvement Exam.
Improvement exams are for students who have passed but are not satisfied with their marks and are willing to take the exams again.
CBSE Improvement Exam can be taken in one or more subjects in the succeeding year only after passing the subject in Class XII.
The examination would take place in the following year.
A candidate cannot appear for improvement examination in the subjects which he/she failed to pass.

Feel free to comment if you have any doubt
Good luck