Heavy metals can be removed by using Aluminium-based coagulants. There are also other ways like using Iron/iron oxide based coagulants, zeolites etc. but they may be expensive compared to Aluminium-based coagulants.

Thanks Dr Satya Vijaya Kumar.

Heavy metals can be removed from waste water by the method adsorption. The metal contaminant gets adsorbed to the surface of the adsorbents i.e ( the medium ) and gets removed.

Activated Carbon can be used as adsorbent for removing heavy metals.

The removal of the heavy metals depends on the concentration of the heavy metals. if the concentration is too high usually by varying the pH the heavy metals can precipitate. but as Anusha has mentioned adsorption is a good way of removing trace amounts of heavy metals. conventionally activated carbon is used. But now a days a lot of research on more environmental friendly and low cost adsorbents is being done. 

Other methods are the application of zeolites and of zero-valent iron. Zeolites incorporate them in their crystal structure whereas zero-valent iron is oxidized to iron hydroxides which co-precipitate several heavy metals either by adsorption or incorporation into their (amorphous or crystalline) structure.

heavy metals will sorb to some solid surfaces (suspended solids) that can settle out, and can also adsorb to dissolved natural organic matter (DOC) which gets removed in flocculation. Any process will have a certain removal efficiency, so the concentration left after treatment is also a function of the starting concentration.  If there is excessive loading of a metal, one has to look at the efficiency of removal of the current treatment process and then decide if additional treatments, such as KMnO4 or PAC or something else should be added to the treatment train

Are you dealing with a conventional water treatment plant (flash mixing, flocculation seimentation and filtration)? In this case, some of them can be removed by adsortion during the flocculation/sedimentation process. It will depend on which heavy metal you are dealing with, and on its concentration in the crude water. Controlling its removal and its concentration in the treated water can be an unpleasant task for the operators! In a real case of water-suply system, the best thing to do is avoid its presence in the water by controlling the environment of the watershed. 

Thanks all for your contributions.

The first part of your question has many answers as have been pointed out by others above. Although ion exchange would be far more appropriate than using GAC. The second part of your question is different. The hydroxide of heavy metals have a minimum solubility point. Therefore there is a pH at which most of these metals precipitate. The concept is very common. You can search for pH vs solubility curves and can find charts that show you the lowest solubility points of metals. Typically, NaOH is added to achieve this pH in the case of single metal, or to reach a pH with acceptable solubility of each of the cluster of metals, based on the discharge limits. After this is done, you add chemicals to floc the particles, or if a batch process, give it a few hours to settle, then filter press the solids.

By three main means:

1-adsorption as of activated carbon, 

2- CNT but expensive and consider as new technology wherestill people are not familiar with yet

3-aluminium based coagulant 

For sure you have to finf out the concentration and pH temperature, agitation  etc

I go with what the other esteemed researchers mentioned about using powdered activated carbon or adjusting the pH of your waste water to the range of  giving precipitation for metals hydroxides and then remove by filtration.

By using ion exchangeable materials like zealot as adsorbent material

It can be removed by filteration, Activated carbon filters can be employed for this,

I have faced this problem recently, so I send you some practical data obtained from my studies. The problem was the possibility of presence of Cr, Fe, Mn, AL, Cd, Cu, Pb and Zn in the crude water, so my tests were to see the possibility of removing them by flocculation, sedimentation and filtration. Cr, Cd and Pb were not removed at all, while Fe, Mn, AL, Cu and Zn were addequately removed in such a way that the remaining concentrations became acceptable to potable waters.

Removal is not all-or-nothing.  Coagulation, flocculation, filtration will remove a certain percentage of metals, and the % removal of each metal may depend on the coagulant used, and other factors such as pH, TOC (amount and type of natural organic matter), other chemicals used and possibly other factors including water temperature.