Many of the resources presented here can be found in the helpful list in Gordon Fee's New Testament Exegesis: A Handbook for Students and Pastors.
A "lexicon" is basically a dictionary, but Biblical lexica usually contain English-language definitions of Greek words, followed by a list of chapter-verse citations to uses of the word in the Bible. The entries are much more extensive than what you would get from a dictionary.
Works that focus on translation choices, historical versions of the Greek text, and other such matters will be quite valuable to students working with the New Testament in Greek.
A concordance is essentially an "index": a list of the verses in which certain words appear. Greek concordances help users find words in the original Greek New Testament, or in English with Greek translations. Some of the tools on the Blue Letter Bible site, at right, are great interactive versions that serve the same function.
These resources will aid you in making your own translation from the Greek.
These works focus on grammar as it pertains to translation.
Understanding how words function within sentences is an important element of exegesis. Many students have not spent a lot of time learning English grammar, so these works may be helpful to you.
Analysis of argumentation and style can be a cornerstone of exegesis, and is an important part of understanding the use of Greek.
Studying verse units and complete thoughts is another of many lenses for good exegesis. Parallel passages fit into this category.