Algorithms which are purely computational are only pseudo-random number generators (pRNG). However, they are a good start. Two commonly used algorithms are linear-congruent (LC RNG) and linear feedback shift register (LFSR RNG) - search 8052.com and/or the net for details (wikipedia has a lot of information).

Although there are more "serious" pRNG algorithms, often based on cryptography, not without reason; nevertheless, none of them will guarantee you what you require - the sequence they generate are deterministic. You need either a physical source of randomness - some sort of noise, or a "human" input, or some sort of communication from a connected but independent system - and "mix" it into the pRNG's stream in an appropriate way. If you have some nonvolatile memory in your system, you can use it as a method for continuous pRNG stream generation across power down periods, avoiding the problem of inadvertent improper "seeding" upon powerup/reset.

There's much more to good RNG than what was said above, but this should give you at least the basic ideas you asked for.

As Andy said above, search this forum, this topic has been discussed in details many many times.

JW