I have attached a jpeg of what I believe is the equation (since I can't write fraction bars it would be really messy). I''m not 100% sure its correct so you might want to check yourself.
In the equation, m1 is the relativistic mass (mass while its moving), m2 is the mass at rest, v is the velocity of the object whose mass you are measuring, and c is the speed of light. The mass is given in kilograms and the velocities (of the object and light) are given in meters per second.
This equation also helps demonstrate, at least in a mathematical way, why it is impossible for an object with mass to move at the speed of light. If you closely examine the equation, you'll notice that at very slow speeds v^2 over c^2 will equal a very small number. At very high speeds v^2 over c^2 will equal a higher number, but it will never go over one (unless you were going faster than the speed of light, but to go faster than the speed of light you would have to go at the speed of light for at least a very small time while you were acceletrating).
At low speeds since v^2/c^2 is a small number, 1-(v^2/c^2) would equal a number only slightly smaller than one, like 0.999999999999967
The square root of that is even closer to one. 1/the square root of 0.999999999999967 would equal a number only slightly larger than one, and therefore when you multiply the object's mass by that number the mass doesn't change that much.
At high speeds since v^2/c^2 is a number only slightly smaller than one, 1-(v^2/c^2) would equal a very small number, like 0.000000000000067
The square root of that is slightly larger (but still a small number). 1/the square root of 0.000000000000067 would equal a very large number, and therefore when you multiply the object's mass by that number the mass increases a lot.
If you were moving at the speed of light, then v^2/c^2 would equal one (300,000,000,000/300,000,000,000). 1-1 is 0, and the square root of 0 is 0. You would then be dividing 1 by 0 which you can't do in math (you can't divide any number by 0).
As far as the relativistic effects on an object, yes the object would undergo a process called elongation. I don't know the equation for it but you can probably find it if you google it. It is similar to the mass increase in that at small speeds you only elongate slightly (so small you wouldn't even be close to seeing it with your eye or even an electron microscope), but the closer you move to the speed of light the more you would elongate. Every part of you that is moving would elongate including your eyes, so you wouldn't notice it yourself. Only people that are standing still or moving slower than you would notice.
There is a really good howstuffworks article regarding relativistic effects:
http://science.howstuffworks.com/relativity.htm
Forgive me if any of the above infomation is incorrect, but I'm only 15 years old.