Can I use an adapter to convert a 120v outlet to 240v?
No. That 120V plug can give small amounts of electricity, like to spin the drum or run the blower.  Normally the heat comes from gas.  

What you bought there is an electric dryer.  That thing requires INSANE amounts of electricity, and the little 120V plug cannot possibly provide it.  

You can search the room (or other potential places where a laundry room would have made sense) for a large socket the size of your fist.  It either has 4 slots...  or 3 slots and looks like the scary clown from Halloween. (And it does kill people). 

If there is no such socket on the premises, and you don't own the place, talk to the person who does.  If you own it (or have permission) then you will need to call in an electrician to install the large circuit breaker, wiring and socket. He will also change the cord/plug to 4-prong, because 3-prong is illegal because it's unsafe.  This is serious work, and should not be attempted by a DIYer new to electricial work.  Success will depend on  


your service panel being modern enough (FPE or Zinsco is no-go), 
panel being large enough (not full) and 
your electrical supply service being large enough (most likely it is, but mine isn't). 


If none of this can work out, then back to the store it goes. They should not have sold it to you.  

If you bought this thing used eg. On Craigslist, then you made the common mistake of not checking what power it takes.  I regularly score very low prices on 3-phase shop tools, because the seller bought it without thinking about power requirements (because he didn't know anything about power) and I go "heh heh heh" as I cart it off. Often he had bought it from someone else in the same pickle.