I will occasionally get the feeling that I am "floating" through life, and this observation is only brought on by my occasional clear awareness that "this is all real."
When this happens, I'll often look at my hand, then around my environment, and be like "Shit, this is all real." It's a fantastic feeling, and can definitely be experienced willfully. After writing that, I am doing it right now.
It's so easy to fall into the routine and normalcy of life; it's almost like one isn't living, but instead floating.
Concentrating and clearing the mind is also a great way of achieving a better grasp of the notion that things are real, and help stop one from "floating."
Parts of this post may not make sense. In my head, and life, I have experienced moments of extreme clarity where I will have an experience similar to an epiphany, with the result being crystal clear awarness. In a sense, it's a reality check, but on a much more serious level.
In general, I think people have too much going on in their lives. Too many thoughts, too much stress, too many ideas bouncing around in their heads. The end result is a looser grip on reality, in the sense that they lose focus on their core selves, and the reality that they are a part of every single day.
One could argue that the stress, numerous thoughts, and general distance from the base reality is in itself reality, but in my experiences, the moments of clarity one experiences when they just clear their mind and concentrate is amazing. It truly feels real. Simple, but very, very real.
There is a good kind of "floating" that can be experienced though. Play some classical music and let it envelop you. I'd recommend Mozart or Haydn. You'll float right away, and results may vary, but I find the experience fantastic.