There is no requirement for people concentrating in Philosophy to write an Undergraduate Honors Thesis; some people do so, many people don't.
To write a thesis, you need a topic and an Advisor and a suitable amount of time. There is no single model to follow, but one standard approach is this. You'd work on the thesis during the two semesters of your Senior Year. In the first semester, you might work through a reading program with the advice of your Advisor, meeting with her or him three or four times in the semester and writing two or three pieces of work—for example, discussions of existing publications in the field and sketches of your own responses to them. Over the break you'd pull together a plan for the thesis itself. In the second semester, you'd write a first draft of the thesis and then a final draft—expecting, of course, that you would continue to do some new reading, and that you might need to be flexible with your original plan. The thesis itself is due about April 15th (or more exactly, two weeks before the Friday on which the Reading Period begins).
It is possible in principle to choose a topic which you don't know much about in advance; but typically the result of that is that you have to spend a larger amount of time reaching base camp, so to speak—getting a decent grasp of existing approaches to the topic—and you have less time for heading up to the summit—developing ideas of your own. Many of the best theses come when a student has already got some idea of a problem area, e.g. from a 100-level course that might have spent a week or two on the detailed topic in question, and might have introduced the class to materials and methods used in related areas that might constitute a useful tool-kit for this topic too. If you already know a bit about the existing approaches to the topic, but have a feeling that you're not quite satisfied with any of them, then you're probably in a good position to go deeper into it, researching further proposals from other people and working out a distinctive contribution of your own.
When you have a first idea of the area in which you'd like to work, you can approach a potential advisor direct, e.g. by e-mail or in Office Hours, or you can discuss the matter with your Concentration Advisor, who should be able to point you towards Faculty Members with interests in areas close to your proposed topic. Don't let your ideas become too fixed too early: often a good discussion will leave you thinking of unexpected directions you'll want to head off in. The normal time for approaching an Advisor is in the first week of the first semester of your Senior Year (or a few days earlier), or at the end of the last semester of the Junior Year.
The standard thing is to register for a reading course, Phil 1990, Independent Studies, either for the first semester alone or for both first and second semesters, with the permission of the Advisor in question. (Note that Phil 1990 takes on a different section number according to who the Advisor is.)
You can register for Phil 1990 just for one semester (followed by registering for either 3 or 4 classes in the other semester). Alternatively, you can register for Phil 1990 for a second semester. Which you do is a matter for negotiation with your advisor, taking into account, e.g. the number of meetings, and the amount and scope of reading and writing that is done. Obviously the work-load for a Reading course needs to be about the equivalent of a normal course.
Length of Thesis
There's no standard length, but 40–50 pages of carefully-argued material would for many topics be a good target.
Two copies of the Thesis are due by the Friday two weeks before the Friday on which the Reading Period begins, which will usually fall close to April 15th. They are to be handed in to the Thesis Advisor. Theses should be computer-printed, on one side only of paper; they do not need to be bound. Some people like to present them in a special folder or binder; this is fine, but not required.
There is usually no oral defense of the thesis. The Thesis Advisor will normally be one Reader of the thesis; there will be a second Reader too, appointed by the Concentration Advisor in consultation with the Thesis Advisor.