There's a difference between leading, and being assertive. By being assertive, am I to assume you mean that you would like to be more "asserting" (def: to state or declare positively and often forcefully or aggressively)

In other words, you want to speak up more often?

Step 1: think of relevant comment
Step 2: open mouth
Step 3: say thought from step 1

Really, it comes down to just taking action. Kind of like going to the gym, or asking a girl out: eventually you have to man-up and just do it. So what if you're wrong, or right? If you're wrong, as long as you're not totally off-topic, it shows you're at least paying attention and thinking. If you're right, it gets noticed.

The big thing is learning when and when not to back down. lots of blowhards like to pontificate upon themselves. If it's the boss, fine let him. If it's a coworker, if he's looking like an idiot, let him. If someone is stealing your words and trying to claim credit, I wouldn't back down. Usually something that points out his rudeness works well, such as, "I'm sorry, was I finished?" Or "I thought I was speaking, but apparently I was wrong." And sometimes, a short but rude "I'm not done" works well. Point to the interrupter at the same time.