WordNet (r) 3.0 (2006):

go about
    v 1: begin to deal with; "approach a task"; "go about a
         difficult problem"; "approach a new project" [syn: set
         about, go about, approach]

Moby Thesaurus II by Grady Ward, 1.0:

181 Moby Thesaurus words for "go about":
   about ship, accept, assume, attack, attempt, back and fill,
   bat around, bear away, bear off, bear to starboard, beat,
   beat about, become public, box off, break, bring about,
   bring round, buckle to, bum, buzz about, cant, cant round, cast,
   cast about, change course, change the heading, circle, circuit,
   circuiteer, circulate, circumambulate, circummigrate,
   circumnavigate, circumvent, close the circle, come about,
   come forth, come full circle, come out, compass, count ties, cycle,
   describe a circle, divagate, double a point, drift, embark in,
   embark upon, encircle, encompass, endeavor, engage in, enter on,
   enter upon, fall into, fall to, fetch about, find vent, flank,
   flit, fly about, gad, gad about, gallivant, get about, get abroad,
   get afloat, get around, get exposure, get under way, girdle,
   girdle the globe, go around, go at, go forth, go in for, go into,
   go round, go the round, go the rounds, go upon, gybe, gyre,
   have at, have currency, heave round, heel, hit the road,
   hit the trail, hobo, issue, jaunt, jibe, jibe all standing,
   knock about, knock around, lap, launch forth, launch into,
   lay about, make a circuit, meander, miss stays, mooch, move into,
   nomadize, orbit, peregrinate, pererrate, pitch into, pivot,
   pivot about, plunge into, ply, proceed to, prowl, put about,
   put back, ramble, range, revolve, roam, round, round a point, rove,
   run about, saunter, see the light, set about, set at, set forward,
   set going, set to, sheer, shift, skirt, slew, spin, spiral, spread,
   spread about, spread like wildfire, straggle, stray, stroll,
   surround, swerve, swing, swing round, swing the stern, swivel,
   tack, tackle, take on, take up, throw about, traipse, tramp, turn,
   turn about, turn around, turn back, turn round, turn tail, turn to,
   undertake, vagabond, vagabondize, veer, veer around, venture upon,
   walk the tracks, wander, wayfare, wear, wear ship, wheel,
   wheel about, whirl, wind, yaw