Deep breathing helps, as does finding friendly faces in the audience and trying to talk to them, as does practicing at home. But there is also something technical you can do beforehand to make sure you are totally prepared and ready to bring the awesome.
One of the biggest problems when reading aloud is that when people are nervous and confused, they rush. If you are rushing, mumbling or fumbling, you will lose your audience. This EXCELLENT advice on slowing down was given to me by the very sensible Bella Stander, founder of Book Promotion 101. (For the record, Bella herself got this advice from her son's bar mitzvah coach. So it is not only useful, but approved by G-d!)
MAKE A READING BINDER
* Decide the section(s) you want to read ahead of time. 90% of authors seem to be seeing their books for the first time when they are asked to read. Confusion reigns - what should I read? Where should I start? What who where wha???! Remember, your goal here is to get people to buy the book, not just read it aloud to them - short and sweet is better than long and disjointed, and it's GREAT to end the section with a cliffhanger "and then what happens?" moment.
* Type this selection (or cut and paste) into a clean document. This will also give you the opportunity to edit anything you don't want to include - like if there are references to something that the audience won't understand at this point, or story spoilers. You don't want to have to interrupt your own reading to explain what so-and-so meant by such-and-such, and the audience won't know or care that you skipped a bit.
* Make the font BIG - 18 point type or so, and give each paragraph its own page. The big font and space means you'll be able to see very clearly, you'll be able to look at the audience more and keep your notes further from your face, and you'll be forced to slow down to at least go to a new page between paragraphs.
* Now take these pages and put them in plastic sleeves in a loose-leaf binder, and read from THAT. The binder and plastic sleeves mean the notes won't get mixed up and you won't have to fumble for the section you want, and it will be ready for you at a moment's notice... and use anti-glare plastic in case there's a spotlight on you at a podium.
Personally, I love it when people read a few SHORT selections, as I tend to drift off/get bored after a few minutes of straight reading. Luckily, your nifty new Reading Binder can include a variety of selections from the book. Also, if there are fans who know your work well in the audience, you might consider not just reading from the new book, but also giving a sneak peek at whatever you are working on next -- no spoilers of course, but teases can be great fun.
Now go make that binder - don't forget to breathe - and happy eventing!