just know the forward voltage drop and subtract it from the voltage you are supplging and given the max amount of current for your leds use ohms's law
V=IR.

http://www.cmiyc.com/tutorials/led-basics/
http://www.kpsec.freeuk.com/components/led.htm
How about looking at this first?

There is youtube vodeo for that.when i also used to have the same problem dwnloading arduino ide and later came to know about the similarity with compaq modem.

How could i combine them?

If you had two recipes to make cookies, how would you combine them?

can't we run them simultaneously through a single sketch.

First you write a sketch.while uploading the sketch of course you nedd computer but while running the program you just need to provide the power supply which can be external i.e apart from computer too.and everytime you power the arduino it operates the code automatically
 

You can not make such a strong magnet from a 9V battery.
You only stand a chance of levitating a small spherical object pliers is right out.
If you use AC it must be rectified into DC to keep the fielding the same direction.

http://uzzors2k.4hv.org/index.php?page=magneticlevitation
This site has the actual project.Ok here he is using 12v and he is able to leviatate the pliers.
Among other questions what should be the length of the wire?How should we coil the wire?

I was doing some project on magnetic levitation and was to require an electromagnet.So i was thinking og making an electromagnet which was strong enough to levitate a pliers.So how can we make such a strong electromagnet out of 9v battery?Can we use AC power supply for this purpose and and how long should be the length of the electromagnet and wire to be used?

http://www.allaboutcircuits.com/vol_3/chpt_4/6.html
If this would be helpful!

I was doing some simple arduino project which was involving the knowledge of logic gates.So I first thought of dealing with logic gates before doing the project and came to know about the pull up and pull down resistors.and my question is "Is the circuit possible without using pull up and pull down resistors?What will be the outcome of glowing leds using simple AND or OR gate without using pull up and pull down resistors?"

try resistors using ohms's law which states E=I*R,know the input voltage and the current that the device can handle ,such as for glowing the leds you should first know the max amount of current the leds can handle and the input voltage you are getting from the arduino pins and you can easily calculate the resistance.For more info
http://www.kpsec.freeuk.com/components/resist.htm

uno ,
motor shield ,ethernet shields,Xbee,gyroscope will be useful.

http://electronics.howstuffworks.com/led.htm
Some informations on how the leds work..

and this is good one too
http://www.kpsec.freeuk.com/components/led.htm

can we amplify the voltage to hundreds of volt by using transistor from the 9v or any small voltage source  and therefore can use it for running televisions and other devices?

Amps multiplied by volts is a constant.

If you multiply the volts by 100 you'll get 100 times less amps - not enough for a TV.

does it mean that if we are gaining the certain amount of volatge from transistor then we are also decreasing the current from transisitor by ceratin amount?

can we amplify the voltage to hundreds of volt by using transistor from the 9v or any small voltage source  and therefore can use it for running televisions and other devices?

I think NASA can make it.the battery that are being used in mars rovers last for almost 20 yrs.if there will be a competition,nasa will make it.