If you just throw something forward, it will coast at a constant speed, whatever speed it had when you let go of it. That's because after you've released it there's no longer any force acting on it, and by Newton's first law that means no change in speed.
If instead you continue to apply a force to it, constantly accelerating it, you will find that it gets closer and closer to the speed of light but never quite reaches it. The same force produces a smaller acceleration as the speed of the object increases. That's not what you'd expect from Newton's second law ##F=ma##, but it turns out that Newton's second law only works for objects that are moving slowly compared with the speed of light (which happens to include everything in our daily experience, which is why we still use it).
A detailed explanation of why this happens requires learning some of Einstein's theory of relativity. You'll often hear that it is because "Einstein says that mass increases with speed". That's a good enough answer for now, but you should be aware that it is not quite right and you'll have to unlearn it if you want to move beyond a superficial understanding of relativity.