I. Relax into your meditation
Relaxation helps you relieve tensions in your body. But meditation goes deeper.
Conversely, one can first do a relaxation exercise to relax the tense parts of the body. Once that is taken care of, it is easier to focus on calming down or observing the pesky mind. A simple relaxation exercise is to mentally scan the body from head to toe and each time you pass through a body part (say nose or thighs, etc), mentally repeat the word relax. The amazing thing about this is that doing this 2-3 times makes me see tangible differences in my state of relaxation. Another way to ease into meditation is to do some deep abdominal breathing. A deep breath is associated with a relaxed state of mind. So the benefits of this goes without saying.
II. Let go of expectations
It would be great if this meditation were perfect - Very calm, no chattering, no worries, no rumination. This statement is fine as an intention. You can have an intention and then let it go. But an expectation is to have this statement run as an under-current hindering your meditation. Since meditation is all about letting go, and yet having an expectation makes you hold on. If in the meditation, the thoughts are running high - So be it. If it is smooth as silk, that's great too.
III. Make it a habit
Habits are powerful. Habits make it easy to do an activity, they make it almost subconscious. So just as you brush your teeth everyday, you just meditate everyday. This makes it easy to meditate when going through rough times. That is precisely when you need to meditate the most!
IV. Sleep well
Meditation is not a way to short-cut your sleep. Good sleep leads to good meditation and the converse is also true (that's why I meditate before I sleep). The way I get to know that I need more sleep is when I start falling sleepy a few minutes into my meditation. Meditation does make you relaxed, but you are also aware. It is a state of relaxed-awareness. Sleep is more like relaxed-unawareness or relaxed semi-awareness.
Hope these pointers help you out - And let me know what helps you with going deeper in meditation.