we did a home exchange a couple of years ago, for a 2-week vacation. i would echo what others said above, that you have some communication beforehand and yet it is a risk. we traded our home in hawaii for an apartment in san francisco. all went well, but i was nervous because there really is no recourse if things go badly. i also agree that where you live will make a huge impact on how much interest you get in a trade.
many traders have mil quarters they use for trading, letting them do more 'non-simultaneous' trades. coordinating dates for a simultaneous trade, as well as getting a good match for location, house size, etc, takes a fair amount of patience and tenacity. okay, actually it takes a whole lot. i used homeexchange.com, and found lots of postings. you can browse there without joining, just to get a feel for the options. check out your own area, too, and get ideas about how you'd describe your place to make it stand out.
someone suggested airbnb, which i have used as a traveler, and we also take guests in our mil unit. unless you live in a very desirable area, maybe near a university or hot business zone, getting a renter for a one-month stay will be challenging. airbnb is more passive than home exchange--you put up your listing and wait. there's no charge for listing on airbnb, and it gets tons of interest and inquiries, so worth a shot.
or, you might find a place to stay using airbnb, that won't be too costly, and won't require having someone in your house. prices vary based on location desirability for tourists. a family home in a regular neighborhood can be a bargain, and they may offer a discount for the extended stay.
have fun with all this!
