Hello aspirant!

For admission process, most of the private colleges ask residence proof in form of domicile certificate. And yes, you can get an admission in a Karnataka irrespective of your original residence. Just sort out the college you want to apply in, then go to their official website, there you'll find their admission dates and also their forms with fee structure and all the facilities. Apply for it, give the entrance exam,clear the cut off, take the branch you wish for. Also make sure, you clear the marks required in NEET too for the entrance. 

Best of luck!

For more queries feel free to ask.