If there are no net external forces acting on your system, then each component of momentum is conserved. You'll have a conservation of momentum equation for the x-direction, one for the y-direction, and one for the z-direction. If you have an object moving in this direction, and another moving in that direction: take each x component of momentum, add them, and conserve the total. Take each y component of momentum, add them, and conserve the total. Another way to say this: the total momentum vector before is the total momentum vector after (equivalent to the "component version")
If there is an external force, the momentum of your system is not conserved. However, the momentum cannot just disappear out of the universe. A block slides on a table with friction. It initially had momentum, then slowed down and stopped. It now has no momentum. Momentum of the block was not conserved. However, it did not just disappear. It's momentum went into the particles of the table. The table particles gained the momentum that the block lost.