I did two sub-I's, one at my home institution and one away, and here are some general tips (some of which were already mentioned
Start thinking about what you want your fourth year to look like. There are a few things you have to accomplish: prepare and take Step 2, do some rotations in your field of choice (in your case, anesthesia), get your application in order, and interview. Some important dates for your ERAS application (from this year, anyway, I guess this could change):
September 1 -- ERAS website opens and you can start filling out your application
November 1 -- Dean's letters released (often when many programs begin looking at applications in earnest)
December 1 -- applications due
As previously mentioned, you should aim to get your application
done as soon as possible, so October should be the absolute latest you do a sub-I if you are looking for a LOR. A lot of my classmates did away sub-i's in the summer. A chapter could be written on how to structure your fourth year, and your school will likely go over this with you at some point in the near future, but generally plan to start the year running, do your anesthesia rotations (and any away electives you are going to use for LOR/"auditions") early; make sure you will have ample time to travel for interviews in the Nov-Jan timeframe; and assess how hard you will want to work in the end of the year.
Look on websites for places you are interested in doing your sub-i. As loveumms alluded to, some schools give preference to their own students or to in-state residents and only after all these students have been placed will they look at other visiting students. Make sure you have a backup plan.
Doing an away rotation can be very expensive. Housing is often not provided by the school and you may be left to your own devices to find a place to live. If this happens, start by checking out the website or call the student affairs office to ask for suggestions. You won't have been the first visiting student, and they likely will have some leads for you. But paying double rent/bills can quickly add up! (Not to mention application fees, gas, parking, ID badges, etc...)
If you are going to do an away rotation, I'd suggest doing an anesthesia rotation at your home program first, so you won't be totally green on your away sub-i. You'll likely need to get LOR from your home faculty anyway.
If doing an away rotation, make sure your school's malpractice coverage is sufficient for the school you are looking to visit. This rarely is an issue, but if it comes up it can end your chance at an away elective (found this out firsthand!)
A basic rule when considering doing an away elective is to be honest with yourself and figure out if this will help or hurt you. If someone is a great "on-paper" applicant with awesome grades, high board scores and a few publications but they come across as a jacka$$/doofus in person, they may not want to do an away rotation at a program they are interested in as it could hurt them. On the other hand, if you are a so-so or average applicant on paper but go to a program, work your tail off, be interesting and engaging, get to know some people in important places, then this may help you get an interview, if not move you up on the rank list. As I said, be honest with yourself--you will be in a different city, know no one, not know your way around the hospital and will not know "the system" so if this is going to ruffle your feathers too much, you may want to rethink doing a sub-i at your first choice program--think instead about going to a strong, well connected "name" program that may not necessarily be your first choice. You will be able to get good letters, but if you bobble the rotation, you won't have shot your chances at your top program.
Sorry for the long post--too much coffee with dinner tonight
and battling insomnia--but I hope this helps!