Use an OUTLINE -- thoughts must progress logically from one to the next. Draw a picture of your thought processes -- straighten out loops.

Start off by posing a specific question.  There must be some reason why you want to research your topic -- specify that reason and crystallize it into a very narrow question.

Do not waste space with plump generalizations. (Did Celtic women fight? NOT:  War is hell.)

Argue in a logical manner, so that one sentence follows reasonably upon the one before.
Paragraphs should have a coherent internal structure as well as funtioning logically to advance your argument.

Do not be sidetracked into irrelevant tangents. Stay focused, on topic and precise.
Use active, action verbs; avoid wishy-washy passive and conditional constructions.

Give examples, explain and describe. Be specific. The bulk of your paper should consist of FACTS.

Do not feel that you need to write down everything you can dig up about the subject; be selective and present only material germane to your argument. If there is evidence refuting your argument, be sure to provide that as well.

Avoid vague generalizations (e.g., Since the beginning of time ... ) and all fluff (e.g.,  It is important to note that ...  )!
Quality counts; quantity counts for nothing if it has no substance. 

Do not repeat yourself. Redundancies indicate disorder and lack of clarity. If you find you are repeating yourself, go back to the outline and refine it.

Make sure that your conclusion has some connection to your opening question. Your paper should progress logically from query to resolution of some kind. Do not wander off into universals, etc. (e.g., Based on the evidence presented, some Celtic women appear to have fought, NOT: War is hell.)

It is perfectly okay to conclude that you have inadequate data to answer your question with certitude; in that case, you should summarize the direction your data have pointed you and outline a potential research plan.

Cite the sources both of passages you quote verbatim, and those you paraphrase. Paraphrase or incorporate as much as possible -- quote verbatim very sparingly. Make it very clear when you are using someone else's work.

Choose a form of citation and stick with it -- be consistent.

... very important is the human-headed horse (Kruta 1991, 535).

... the behavior of the Greeks at this time has been compared to that of "fractious, ill-mannered children" (Green 1990, 288). This assessment ...

- or, avoiding the passive verb  -

... Peter Green compares the behavior of the Greeks at this time to that of "fractious, ill-mannered children" (1990, 288). This assessment ...

Bibliography contains these entries:

Green, P. 1990. Alexander to Actium. London: Thames and Hudson.

Kruta, V. 1991. "Celtic Religion." In The Celts, O.H. Frey, V. Kruta et al., eds. New York: Rizzoli. 533-541.

Caesear, de Bello Gallico, trans. V. Kruta.

Your bibliography formats can be different, as long as they include the relevant information and are consistent.

... the behavior of the Greeks at this time may be compared to that of "fractious, ill-mannered children."¹

^{--------------------------------}

¹ Thus Peter Green, Alexander to Actium, (London: Thames and Hudson, 1990), 288, in a somewhat extreme formulation.

Be consistent; if you do not feel comfortable with standard abbreviations (in the Oxford Classical Dictionary), use the authors' full names. Name the work and the translator, and make sure to include your source in the bibliography.

As a captive slave slips away
from a rich house, whom fate has recently deprived
of her native land, [ ...]
so the lovely girl
rushed forth from the palace. For her the bolts of the door gave way
themselves, leaping back at the shrill strains of her magic song.
(Apollonius of Rhodes, Argonautika IV, trans. B. Fowler)

If you quote a long passage (4 lines or longer), use a block quote -- no quotation marks, and indent the block on both sides.

If you use the historical present ("Celtic warriors are ..."), do so throughout. Note that the sources you quote may use a different tense; remember to return to the one you have chosen.

No-one is. Neither .. nor ... is. The number of houses is. The ages of man are.

"At the age of three, Green states that Alexander the Great ..." means that Peter Green was three years old when he said it.

"Having been destroyed by an earthquake, the inhabitants of the town began to rebuild" means that the inhabitants were destroyed.

"While walking along the broad avenues, the city made a big impression on her" means that the city was doing the walking.

Punctuation:

This is so; this is also so and is logically connected.
(two independent clauses)

This is so; however, this is different
Although this is so, something else is differently so

At a time or place, this is so
This is so at a time or place

I did this, which was good
I did this, although I shouldn't
(main clause, dependent clause)

I did what was good
I saw that he had done this.
(no comma)

Verbs and Subjects:

This being so, something else is so
He having done this, I did something else
but -- same subject: Having done this, he did something else
Seeing him do / Doing this, I did something else

I saw what he had done (before)
I saw what he was doing (at the same time)
I see what he did / has done / has been doing (now)

Avoid split infinitives -
  to speak loudly; loudly to speak -- NOT to loudly speak

Prepositions and misc.:

NOT inside of, outside of, (near to)
Just inside, outside, (near)

with which I did (NOT which I did with)
with whom he spoke (not that he spoke with)

the person who
the thing that -- not the person that

Vocabulary:

Look up words if you are not sure what they mean -- highfalutin' terminology is fine as long as it's the right word in the context.

Avoid slang; e.g., instead of "being that," use "since" or "because" ...

    - a situation, person or data imply (= suggest) something; a person infers (~ deduces) something based on the data ...

The  preceding are only the most common pitfalls.

Use the Writing Center to help you identify any problems you may have.
Use the OWL at Purdue, esp. for Grammar and Mechanics.
When in doubt, consult Strunk & White, The Elements of Style (multiple copies in UT libraries, downloadable audiobook, at HalfPrice ...)

Lay your writing aside for a few days and look at it again with fresh eyes.

Have a friend or classmate go over it with you.

ALWAYS read your paper aloud, whether to a friend or yourself.

Proofread your work! Sloppy errors show carelessness.