How to get a synthetic cork back in a wine bottle?
There is no trick, it just won't work. Synthetic corks are popular as replacements to cork not only because they are cheaper, but more effective at preserving wine as they don't dry out, and they expand more in the neck keeping a tighter seal. This makes it more difficult, if not impossible, to get them back in. 

The simple and easy solution is to buy re-usable bottle stoppers. There are many different types, I prefer the ones which have a lever or button you push down to expand the stopper as they are best at preventing spills and leaks. There are vacuum sealers as well, however IMHO they're gimmicks and don't improve the storage of wine.