How long does it practically take to increase credit score from 600 to 800?

Yes you can raise your credit score by 200 points. But for that you must know the reasons behind why it is so low...
So, you need to check your free copy of credit report and work on to fix the problem. You may inform the issue to the reporting agency — Equifax, TransUnion or Experian with proper documents. Disputing errors on a credit report can help raise your credit score.
Apart from that, you may have to pay all the creditors who will delete their filings on your report. Next, focus on paying the credit card bills.
Getting a secured credit card may also work well in this case.

Increasing credit score is not a matter of 1 or 2 days. You have to keep patience and manage your credit cards responsibly to see the changes. Pay your credit card bills in full and within time. Pay all your monthly bills on time. Also, you have to stay within your credit limit to increase your credit limit sooner.

Depends on several factors. If you can lower your credit utilization ratio to 30% or less than that, then you can expect to a sharp rise in your credit score. A high credit utilization ratio indicates that:

You're not making enough money for repaying your bills
You're not good at managing money
You make bad financial decisions

Don't expect a miracle. Use the tips suggested by Tiara and Sanders. It will take a few months to increase your credit score by 200 points.