As an Indian citizen planning to migrate to the UK, what is the best way for me to hunt and apply for jobs there?

UK is ideal location for the people who are keenly looking for success and growth in the career.  For the work visa, it has different criteria, requirement and qualification to apply in the UK. Some companies want to clear ILTES and TOEFL  competitive test to check english fluency.  Now, the procedure to migrate has been changed. You can either apply online or offline as per your convenience. Rest of the things leave on them as they will help you to fill the form and drop the application to apply. You can Contact https://www.visasimple.com  company as they are leading immigration consultancies and help you to how you can settle in the UK.  

The  UK  government has an occupation "shortage list "; it's on the Internet.  It may be easier to get a job in one of those fields.  Occupations on the list includes; physics & chemistry high school teachers, chemical engineers, PhD scientists, mechanical engineers & civil engineers working in oil and gas, subsea & offshore engineers, doctors working in emergency medicine or in psychiatric medicine, self employed lawyers, & certain  jobs in acting. There are a few others. Can't remember what they are. In addition you are exempt from UK immigration control if you can find a job paying more than £ 150K per year; or you have £2million  sterling to invest. Jobs paying more than £ 150K per year in the UK includes senior doctors ( Eg Hospital consultants ), finance directors, management consultants, dentists (some), some jobs in oil and gas, some IT jobs, some jobs in advertising, ceo's, footballers, senior executives in multinationals, some pharmacists & optometrists, some entertainers, partners in accountancy and law firms, investment /merchant bankers, stock brokers.

In general, unless you have super-skills or significant funds to invest, I visualize you facing hurdles as a non-EU national.