How should I fix blemishes in a stained particle board table top?
It would help to know exactly what you want to accomplish because there's likely a better finishing method than stain in your situation. A good first step is a paste wood filler to smooth out the surface imperfections. You may need to shop around a bit or online, and it's helpful to decide on a finish first.

Paint is the easiest solution, any you have some flexibility with sheen and texture if you open your options to chalk and milk paint. That being said, many people don't care for painted furniture and "stain" is often a code word for wanting a clear topcoat which is problematic with paint.

Lacquer is much more common than paint for factory finishes. It's not brush friendly but you can buy it in spray cans. On its own you'll get a durable fingernail polish type of finish, while preserving the option of adding a clear lacquer topcoat.  

For problem pieces a gel stain is a much better option than stain conditioner. They're thicker than conventional stains so they don't absorb unequally. The advantage for you would be the ability to apply polyurethane as a topcoat. It's also much more rag and brush friendly than lacquer.