Yeshaya 58:13 states that Shabbat is called oneg (delight). I have seen several different items described as oneg shabbos including taking a nap, marital relations, enjoying food at the shabbat meals and refraining from work. I would like to know if oneg simply means anything that a person enjoys in which case, for example, reading a book could be oneg shabbos. Or, if there are any halachic criteria for this concept.
The Vilna Gaon writes that the definition of oneg shabbos is the enjoyment of things on shabbos itself, in contrast to kavod shabbos which is the all the preparation one does before shabbos.
Rav Ovadia Yosef in Kitzur Shulchan Aruch (רמב) says this explicitly as well:
As an example see the Remas comment on the Shulchan Aruch (או"ח שו-א) regarding ודבר דבר, the manner of speech on shabbos should be different than from the week:
א. ודבר דבר שלא יהא דבורך של שבת כדבורך של חול הלכך אסור לומר דבר פלוני אעשה למחר או סחורה פלונית אקנה למחר ואפילו בשיחת דברים בטלים אסור להרבות. הגה: ובני אדם שסיפור שמועות ודברי חידושים הוא עונג להם מותר לספרם בשבת כמו בחול אבל מי שאינו מתענג אסור לאמרם כדי שיתענג בהם חבירו (תרומת הדשן סימן ס''א):
The Rema says that if one derives benefit from telling over news and stories, it is permitted to speak about it on shabbos. However, if one does not enjoy this manner of speaking than it is forbidden.
Regarding reading a book for enjoyment on shabbos, the Rabbi on this site seems to qualify enjoyment on Shabbos as to be only something that is constructive and positive eg. reading a history book in order to see the ways Divine provedence:
The Mishna Berurah writes (ס' רמא) that when in Yeshaya it says "Shabbos Shabbaton Mikra Kodesh..." that Chazal understand this to mean that one must honor and enjoy shabbos. One honors Shabbos through clean clothes and enjoys Shabbos through eating and drinking nice foods. The M"B continues to say that the typical food which one enjoys is meat and wine, and so there is a concept to have this at his meals. He then mentions that oneg shabbos comes from the eating of "dagim gedolim - big/great fish," and continues to say that one should eat fish at all three meals. However, if one does not like fish, then he should not eat it since it would not bring him enjoyment. He continues to discuss that one fulfills the concept of "oneg shabbos" by having three meals (those who cannot afford 3, can have 2 and must spend other money on obtaining shabbos candles). However, later on (a few simanim later -- in regards to neiros shabbos - shabbos candles) he writes that the main aspect of oneg shabbos is the candles at the meal. So, so far we have discussed eating, drinking, and candles.
In the book, Kitzur Hilchos Shabbos, it brings a nice idea that Shabbos (ש.ב.ת.) stands for שינה בשבת תענג - He will enjoy sleep on shabbos.
There is also, though I can't remember where I've seen it, a concept to have relations on Shabbos. Explained by the fact that the holiness of Shabbos is a suitable time to engage in the holy mitzvah "to be fruitful and multiply" as well as that this is something that brings both the husband and the wife enjoyment.
Finally, in regards to doing "anything," obviously these things have to be within the framework of what is permissible on shabbos. There are other things for which shabbos is a particularly appropriate time for doing them such as learning torah (I can't remember the source).
All in all, we see that there are specific things that define oneg shabbos and contribute to it, but as whole it is a broad category which leaves room for individuality and one's own (kosher) taste.