What are differences between speed and velocity, velocity and speed and acceleration?

Firstly, it is important to know the difference between scalars and vectors. Scalars are just a number associated with a measured quantity, while vectors are a number AND a direction associated with a quantity. Vectors can be represented using arrows, that indicate the direction of a quantity, with its length representing its value. The concept is easier to see with examples:
Distance and displacement both are a measure of position, but distance is a scalar and displacement is a vector. An object's distance of an object from a fixed point can be given simply as a value - 10 meters, 3 inches or 2 miles are all examples of distances. Displacement requires a direction: 10 miles north, which could then be represented as an arrow on a map, for example.
Speed and velocity are entirely similar. Both refer to how fast an object moves, but speed is simply the value (30 meters per second) and velocity is the vector, which requires a direction (30 meters per second, upwards). Acceleration is the rate of change of velocity of an object. It can be given as a scalar quantity or a vector quantity, depending on whether the direction of the acceleration is specified or not.