Before you begin conversations, make sure your profile is completely filled out and you have some great photos. You must complete a percentage of your profile before messaging between connections will be unlocked. This can make all the difference in encouraging another member to connect with you, too.
When it comes to reaching out, compliments are great, but they don't give the other person an easy way to respond other than with “thanks.” You can help your chances at a great reply by letting someone know you really read their profile and are interested in a quality connection. For instance, consider asking a question about one of their interests or hobbies.
If you're struggling to start a conversation you can always try a Nicebreaker! Nicebreakers ask you to both answer a question to help get the conversation started. They are available below any un-started conversation.