You need a pro to come look at it. Ask around for a good chimney company in your area. Something like this needs to be evaluated by someone who can take into account many variables.
The total hieght of the chimney, the chimney hieght above the roofline, makeup air, flue liner condition, smoke chamber condition, size of flue....you get the idea?
Then there is also what else in the house is calling for air, hood vents, dryers , hvac systems and even the time of day and temp outside.
If you want to fix the problem once, ask for someone who gives you these variables as answers.
Another thing to consider is the smoke is not the deadly thing which is comming into your home..it is the carbon monoxide, which is ordorless, colorless and kills.
For this, get the pro to give you the pointers, even if you end up DIY.