When I first started to teach, I would throw kids into the deep end and give them an independent reading assignment (genre, length, etc.) and a week to procure the book. Kids would often wait until the last minute and then check out whatever book in my classroom library had a flashy cover. It didn't take me long to determine that this completely undermined my entire goal for independent reading: for students to read something that they enjoy. I changed my strategy. I decided that if independent reading was something I valued highly enough to assign, I should make certain the goal for the reading was being met and that hinged on students selecting books that were at an appropriate reading and interest level for them.
This activity can take as little or as much time as you might like. I generally spend 30-40 minutes. First, I pull on an excellent resource: our librarian. I let her know what I am asking for: for one class I am looking for high interest texts at their reading level (the goal is to get them to read and that's it) and for my other class I am looking for texts slightly above their reading level that have been made into movies (the goal is to engage them in reading that stretches their abilities a bit and to have them practice the skills of comparing and contrasting one subject in two different artistic mediums - a CCS standard that often gets overlooked). She pulls a cart of books that meet each criteria and I take it to my classroom.
Step two: set-up. I put them desks in small groups and distribute the books equally between each group. When the kids arrive, I assign them table groups (I will need them to read silently and independently and I have found that allowing them to select the groups can defeat that purpose). They are given apx. 1 minute to peruse the books on their table. They need to select one that looks interesting. I time this - they read any part of that book (jacket, middle, beginning, etc.) for two minutes silently and independently. Then they must leave all the books on the table and rotate to the next table group. 1 minute to peruse, 2 minutes to read. Rotate. You get the idea. Obviously, all the times are flexible and can be adjusted to allow for a shorter or longer lesson. I also have experimented with having them write notes on the books they read - title, author, impressions, rating, etc. so that they can use these notes to remember the text(s) they liked.
At the end of the period, the librarian comes in and checks texts out to the students. I usually give about three days and any students who still didn't find what they want are welcome to get a text on their own - I always make them get these texts approved, ensuring that they meet my criteria.
Another resource that I really like to direct students to is the Book Lust series by Nancy Pearl. These provide excellent lists of books that fit all kinds of categories.
Want some ideas for independent reading projects? Here are some ideas that I use: http://roselynrobison.blogspot.com/2014/06/independent-reading-assignment-book.html