Someone just e-mailed me to ask about resources for learning the Aramaic of the Targums (ancient Aramaic versions of the Hebrew Scriptures). I spent a while writing up some suggestions, and I thought I would reproduce them here in case anyone else is interested.
The best grammar of the Aramaic of Targums Onqelos and Jonathan that you will find in print is Grammar of Palestinian Jewish Aramaic by William B. Stevenson (no relation to me). I can't say it's great, but it is adequate if you already know Hebrew or Syriac. It was first published in 1924. The Wipf & Stock reprint (to which the link leads) is decent, and it is certainly inexpensive ($12). Professor Douglas Gropp (Westminster Theological Seminary, Dallas) is preparing a teaching grammar for eventual publication by Oxford Press, but I do not know when it will go to print. The last I heard it is waiting for a serious proofreading.
If you are interested in studying Targum Neofiti, there is a scholarly grammar (a revised doctoral dissertation) called simply A Grammar of Targum Neofiti, by David M. Golomb. It is a work designed for specialists and the Aramaic is all transliterated. You can find copies very cheap.
The most complete dictionary of Targumic Aramaic is Dictionary of the Targumim, etc., by Marcus Jastrow. It is another old publication, but still quite serviceable. I have the Hendrickson reprint (to which the link leads). The text shows signs of having been repeatedly photographed and reprinted, but it is generally legible. It at least has the merit of being affordable.
If you want a more modern dictionary of Aramaic that covers much of the vocabulary of the Targums, get A Dictionary of Jewish Babylonian Aramaic by Michael Sokoloff. It is much more expensive and it covers the Talmud rather than the Targums, but much of the vocabulary of the Targums is in the Talmud, so it is quite useful. Dr. Sokoloff's research is thorough and up-to-date. An even more recent dictionary of Targum Onqelos that just came out is A Glossary of Targum Onkelos by Edward M. Cook. The quality is high, but so is the price.
Once you have a grammar and a dictionary, you can study the Targums by the inductive method. You start reading the text and looking up words and grammatical forms that you don't already know. This isn't quite as easy as having a teaching grammar of the language and learning lots of paradigms and syntactic patterns first, but it is an effective method.
As an aid to your study, you may want to use the English translations of individual books of the Targums from Liturgical Press. Here is a link to the translation of Psalms to get you started. There are quite a few volumes in the series, and they are not cheap.
For the actual text of Targums Onqelos and Jonathan, far and away the best editions are published in Spain. At least some of these can conveniently be purchased through abebooks.com. Some Targum Neophyti texts are also available at abebooks.com.
An older edition is that of Alexander Sperber, but it is expensive and has many errors. However, it may be serviceable for learning purposes. You can also buy individual volumes for much less than the whole 4-volume set.
It just occurred to me to see what Wikipedia had. There are links there to free online editions of Targum Onkelos and a tranlsation! Go to http://en.wikipedia.org/wiki/Targum_Onkelos. I think the Mechon Mamre texts will be pretty accurate. The translation is from 1862, so it may have some defects from the point of view of scholarship almost 150 years later, but it will at least be a starting point.