I've noticed my ability to have these instances increase depending on a few things:
What's going on in the sky, what you surround yourself with, where your head is at, and what you focus on.
I've noticed an increase in psychic abilities whenever I don't have any hard aspects to my natal positioning of Mercury, Moon and Neptune. This is when there aren't any other planets at directly 90 degree or 120 degree angles to my natal positioning of them. (you can look more into astrology when it comes to this, there are different planets configurations that can help lend a hand at psychic ability and others that tend to muffle or block the ability.
-Note also, astrology is a verifiable thing, although not well known in the scientific realms and not credited by the mass convention very often. Although those with satellites know that different positions of planets tend to cause their equipment to malfunction.
(I can post some of the evidence pointing toward this if anyone is really curious.)
I also notice an increase in these moments when I surround myself with positive, and well balanced people. Or people who just vibe with my better half. It seems the 'vibes' they put off tend to help me stay on my own positive path. With a clear head, and without disrupting people around to knock you off your path, I think it helps immensely.
Where your head is at, really ties in to all of it. If you're not in a stressed out discordant place, you may tend to be able to break through to hearing your inner voice and the messages coming to you all the time.
(Although in times of stress you can have important moments of intuitive break throughs at the most harrowing and important moments.) I think though that the moments of intuition that break through such cloudy muddles, and stressful moments come from an already strengthened ability from before. Or else a breakthrough moment coming from something that must have built up subconsciously over time.
It's like working a muscle.
Focused conscious intent, as well as clear headed meditative emptiness help build that muscle.
What you focus on ties in with what I said previously as well.
I've noticed an increase in the ability to remember dreams the more I talk about them with (willing

) listeners, and especially writing them down. Through this process my dreams have become more lucid, more memorable, more detailed and frequent. And that way I have been able to record dreams that I later find out were precognitive.
Using tarot I find also helps. (But be careful to only focus on God, or higher wisdom to help you, not strange entities.) The quantum mechanism involved with connecting with the energy of your answer, the intention involved is exactly like the psychic process. That same 'muscle' is being stretched and worked.
Also, write down your experiences, and you'll start to get a feel for what they are like... you may start to get random thoughts popping up that you pay more attention to, which in turn, you later decide to take note of, and find out that it was a precognitive thought.
Hope this helps!