Telekinesis refers to the ability to move physical objects with one's mind.  There are many techniques that may be applied to achieve this, but the fact remains - TK is hard! Don't expect to be lifting couches and chairs with your mind any time soon; as with anything, TK, even with small objects, takes a while to learn, and many have minimal success.

The easiest forms of Telekinesis occur with an already-moving object, or some event that has a chance (however slight) to happen as you wish it to.  In this way, you only need to increase the chances that the outcome occurs the way you want.  This affecting of probability is called MicroTK.  Moving candle flames and causing electronic equipment to work are examples of this.
MacroTK, on the other hand, involves moving a stationary physical object.  Because you are affecting the object on a physical, tangible level, instead of merely on an energy or probability level, it is much more difficult to get results.  I recommend practicing at least some with microTK first, because macroTK can be frustrating if one does not see immediate results.

There are several methods that may be used; one may work well for one person, and another person may have no results with the same technique.  Try these, but DON'T STRAIN YOURSELF!  Try only 5 or 10 minutes per day; if your head feels like it may start hurting, STOP.
The idea behind TK is focus, not concentration.  You do not need to think hard to do TK; in fact, as with most psychic activities, a relaxed and meditative mind usually works better.  Keeping your mind from wandering, however, is important.
Relax, get comfortable.  Set a lighted candle in front of you; we will try PyroKinesis (moving fire) first.

Method 1:  Becoming One With the Object
Stare at the base of the flame (not at the flame itself, don't get retina burn, and yes, you may blink).  Gaze at it, defocus your eyes and enter a meditative state.  Watch how the candle dances and moves.  Imagine the flame as an extra limb, feel that you are able to move it as easily as your arm or leg.  Keep watching, and when you feel it is a part of you, try flexing it.  See the flame grow wider, thinner, taller, shorter, flicker, or stand still.  Do this for 5-10 minutes, then snuff the candle out.

Method 2: Visualize!
With this method, just see what you want to have happen clearly in your mind.  If you want a parking space near the door of a crowded mall, visualize clearly an empty space right near the front door before you leave your house.  Looking for a special something?  See it clearly, see yourself in possession of it and happy.  To enforce the visualization, write down exactly what you want.  Be descriptive!  If you need it, it will happen.  If not, realize there may be a reason it did not occur as you wished; perhaps something better will come along, or it just wasn't appropriate for this thing to happen at this time.  Always ask that it be done in the best interests of all concerned.  This also works on faulty electronic equipment and many other things; just see the computer/vcr/car/etc working perfectly.

Method 3: Pushing With Energy
Read the beginner logs and master Energy Balls before attempting this one.
Blow up a balloon and set it on the floor (preferably a surface with very little friction; a linoleum floor perhaps)
Form an energy ball, making it as dense as possible.  With the energy ball between your hand and the balloon, push the balloon along the floor with the energy ball.  Do not touch the balloon with your hand.