In the case of UK visas, there is nothing you can do to speed up the process or find out where you are in the processing queue. Even internally they only have 3 or four status indicators.
Telephoning them will lead to a circular maze of recordings and menus. Emailing them (or faxing them, or posting a letter to them) will not produce a substantive result.
Having said that, once their agreed processing target has been overrun, you can then initiate a formal enquiry. Their target in the US is 12 weeks, so if you applied last month, there is approximately 8 weeks remaining before you can enquire.
Also, if you are applying as a family visitor, your UK based sponsors can write to their MP once the 12 weeks has expired. This has the paradoxical effect of slowing things down because they have to find your file and once they find it, the 12 weeks starts again on day 1.
Thus, the net answer to your question is: there's nothing you or anybody else can do until their processing target has expired.