First the places and types of variations together with the
manuscripts supporting each must be discovered.
Consult various translations and look for footnotes which
say something like "Other authorities read ...."
Consult the New King James Version. Variations are
marked with M for Majority Text (Byzantine tradition)
and NU for Nestle-Aland/United Bible Societies Text.
Check commentaries on your passage, especially critical
commentaries like the International Critical
Commentary, the Expositor's Greek New Testament, and
Henry Alford's commentary (the multi-volume set on the
Greek is best).
Check Metzger's Textual Commentary on the Greek New
Testament (some Greek may be required to use this, but
often not).
Check the UBS Greek New Testament footnotes. You need to
use a Greek lexicon or Greek-English interlinear if you
do not know Greek or are just starting in Greek.
Check the Nestle-Aland Novum Testamentum Graece
footnotes. The symbols you need to know are:
A little circle means the word is omitted in some
manuscripts. A little square and later a backslash
means that all the words between them are omitted in
some manuscripts.
A little T symbol means that some manuscripts add
the words here found in the footnotes.
An upper left corner symbol means that some
manuscripts have a different word. Upper left and
right corner symbols mean that some manuscripts have
different words than the ones between the symbols.
Squiggle marks mean that words are found in a
different order in some manuscripts.
In the footnotes the variant readings will be listed
after the same symbols as found in the text; then the
witnesses supporting that reading are given. The
evidence supporting the text is found after the word
txt; if no text evidence is given, it is all other
witnesses.
If none of this helps or if you have trouble with the
last two steps, ask your teacher for help.
Evaluate the external evidence (the witnesses). Also evaluate
the internal evidence to decide which reading best explains
the rise of the others. If the internal and external
evidence conflict, give more credence to the internal
evidence.
Write at least a page on what you have found, giving the
variant readings, the witnesses supporting each grouped by
age and families, and the likelihood that copyists may have
changed one reading to another.