The material is compacted using 'normal' compaction plant. In the UK, once the soils have been treated and rotavated, they will be compacted to a specification, often using a smooth-wheeled roller [even for cohesive soils]. Depending upon the material being treated, and whether or not you are looking at modification [short-term/improve handling/reduction in moisture] or stabilization [long-term/formation of cemetitious product] it will influence the the type of hydraulic binder used. The selection of the binder will also be dependant upon the material being treated. Clay soils high in silica and allumina are reactive with lime and this in isolation may be sufficient for your purposes depending on what you want the result to be. For higher strength, granular or soils with low silica and allumina then cement can be/is used. In addition to this other binders can be used such as PFA and GGBS. I am currently involved with a project where relic sewage sludge is being modified and stabilised using a combination of lime [2-3%] and PFA [12-18%] which is providing a material with a comparable stength in excess of 5% CBR. The material is being treated in order to leave it on site [thus preventing the need for off-site disposal - very VERY expensive in the UK] and is forming non-critical areas under hard cover on site for a larger commercial development.
Going back to the selection of the appropriate bindrs, if there are sulfates present in the ground, these can and will combine with water, calcium, allumina or silica and form expansive products. There are a number of accepted methods for dealing with this, however if you get it wrong, it really is a big problem. Some binders such as PFA and GGBS can help restrict the formation of expansive by-products, but with higher sulfate contents this can still occur. Total sulfates of < 0.2% should be OK subject to appropriate testing, sulfates between 0.2 and 1.0% MAY be ok but it needs extensive testing and sulfates over 1% are not reccomended for treatment with lime and cement.