I like to make it easy and have people enter just by leaving a comment, and then use a random number generator or random list shuffler to draw the winner. It's not as professional as rafflecopter, but you don't have to worry about stuff not going through.
The only other way is for people to leave comments for entries. This is long and sometimes a pain - hence the invention of Rafflecopter. I've used it many times, both hosting and entering and haven't had any problems. Good luck!
I've been hosting book giveaways for awhile, and I like to make my mandatory entry a visit to the author or publisher website, and then asking for contestants to leave me a comment with something they learned or liked on the website.
I also do all sorts of activities for extra giveaway entries, way too many to list here, so feel free to check out some of my former book giveaways.