An open landfill that does not have a leachate collection system caused the pollution (heavy metals and organic compounds) of the ground water in its vicinity. What is the best practice to deal with such pollution?
The best is to excavate and remediate the site and build up a new landfill, of course if you have the resources to do that. If not, so isolating the waste materials from the surrounding environment and in all cases you need to move the waste materials to another place to insulate the bottom lining. Then the leachate should be collected and treated. I am suggesting mining this dump and try to recycle and recover materials and energy as much as possible.
Not exactly my expertise, but a few comments to consider. There are many examples of this, and agencies such as the US EPA has tried to identify and treat hazardous waste sites. I am fairly sure there is literature available to review on a variety of approaches, removal, capping site, phytoremediation, lining bottom, capturing wastewater, monitoring, etc. It is also important to understand conditions of contamination of groundwater, as likely anaerobic, so injecting oxygen may be needed in remediation, or introducing bacteria that can help treat contaminants. It is also critical to evaluate degree of groundwater contamination, how the materials are moving, whether altering pH or other treatments may help participate contaminants, etc. Also, are ther well users that are or may be affected, they deserve notice and help with expenses on testing, securing alternative water sources or suitable treatments before use. There are numerous engineering companies that have tackled issues as you suggest. I would suggest if trying to advise as individual or University, obtain sufficient insurance relative to potential liability.