The Collaborative International Dictionary of English v.0.48:

Establish \Es*tab"lish\, v. t. [imp. & p. p. Established; p.
   pr. & vb. n. Establishing.] [OE. establissen, OF. establir,
   F. ['e]tablir, fr. L. stabilire, fr. stabilis firm, steady,
   stable. See Stable, a., -ish, and cf. Stablish.]
   1. To make stable or firm; to fix immovably or firmly; to set
      (a thing) in a place and make it stable there; to settle;
      to confirm.
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            So were the churches established in the faith.
                                                  --Acts xvi. 5.
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            The best established tempers can scarcely forbear
            being borne down.                     --Burke.
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            Confidence which must precede union could be
            established only by consummate prudence and
            self-control.                         --Bancroft.
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   2. To appoint or constitute for permanence, as officers,
      laws, regulations, etc.; to enact; to ordain.
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            By the consent of all, we were established
            The people's magistrates.             --Shak.
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            Now, O king, establish the decree, and sign the
            writing, that it be not changed.      --Dan. vi. 8.
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   3. To originate and secure the permanent existence of; to
      found; to institute; to create and regulate; -- said of a
      colony, a state, or other institutions.
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            He hath established it [the earth], he created it
            not in vain, he formed it to be inhabited. --Is.
                                                  xlv. 18.
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            Woe to him that buildeth a town with blood, and
            establisheth a city by iniquity!      --Hab. ii. 12.
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   4. To secure public recognition in favor of; to prove and
      cause to be accepted as true; as, to establish a fact,
      usage, principle, opinion, doctrine, etc.
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            At the mouth of two witnesses, or at the mouth of
            three witnesses, shall the matter be established.
                                                  --Deut. xix.
                                                  15.
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   5. To set up in business; to place advantageously in a fixed
      condition; -- used reflexively; as, he established himself
      in a place; the enemy established themselves in the
      citadel.
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WordNet (r) 3.0 (2006):

establish
    v 1: set up or found; "She set up a literacy program" [syn:
         establish, set up, found, launch] [ant: abolish,
         get rid of]
    2: set up or lay the groundwork for; "establish a new
       department" [syn: establish, found, plant,
       constitute, institute]
    3: establish the validity of something, as by an example,
       explanation or experiment; "The experiment demonstrated the
       instability of the compound"; "The mathematician showed the
       validity of the conjecture" [syn: prove, demonstrate,
       establish, show, shew] [ant: confute, disprove]
    4: institute, enact, or establish; "make laws" [syn: lay down,
       establish, make]
    5: bring about; "The trompe l'oeil-illusion establishes depth"
       [syn: establish, give]
    6: place; "Her manager had set her up at the Ritz" [syn:
       install, instal, set up, establish]
    7: build or establish something abstract; "build a reputation"
       [syn: build, establish]
    8: use as a basis for; found on; "base a claim on some
       observation" [syn: establish, base, ground, found]

Moby Thesaurus II by Grady Ward, 1.0:

225 Moby Thesaurus words for "establish":
   acclimate, acclimatize, accommodate, accustom, adapt, adjust,
   advertise, affirm, afford proof of, ascertain, assure,
   authenticate, author, authorize, back up, ballyhoo, bark, base,
   bear, bed, beget, begin, bill, boost, break, break in, breed,
   bring about, bring forth, bring home to, bring to effect,
   bring to pass, bring up, broach, build, build in, build up,
   bulletin, case harden, cause, certify, christen, cinch,
   circularize, clear up, clinch, conceive, condition, confirm,
   constitute, corroborate, create, cry up, decide, declare lawful,
   decree, deep-dye, define, demonstrate, determine,
   dismiss all doubt, do, domesticate, domesticize, effect,
   effectuate, embed, enact, engender, engraft, engrave, ensconce,
   ensure, entrench, etch, familiarize, father, find out, fix, float,
   follow, follow from, form, formulate, found, generate, gentle,
   gestate, get at, give a write-up, give birth to, give occasion to,
   give origin to, give publicity, give rise to, ground, habituate,
   harden, have a case, hold good, hold water, housebreak, impact,
   implant, impress, imprint, inaugurate, incept, inculcate, induct,
   infix, ingrain, initiate, inscribe, install, instill, institute,
   insure, introduce, inure, invest, jam, launch, lay,
   lay the foundation, legalize, legislate, legitimate, legitimatize,
   legitimize, lift up, locate, lodge, make, make a regulation,
   make certain, make good, make legal, make no doubt,
   make no mistake, make out, make sure, make sure of, materialize,
   moor, nail down, naturalize, occasion, ordain, organize, orient,
   orientate, originate, pack, pitch, placard, place, plant, plug,
   post, post bills, post up, prescribe, press-agent, print, produce,
   promote, prove, prove to be, prove true, publicize, puff, put,
   put in, put in force, put up, raise, realize, reassure, regulate,
   remove all doubt, ring in, rivet, root, sanction, season, seat,
   secure, see that, see to it, sell, set, set afloat, set agoing,
   set at rest, set down, set in, set on foot, set up, settle,
   settle the matter, show, sire, sort out, spiel, stamp, start,
   start going, start up, station, stereotype, stick, substantiate,
   support, tame, train, turn on, usher in, validate, verify, vest,
   wedge, wont, work, write up