Your repair options may vary dramatically depending on what is wrong with it, and what the technology used on the card is.
Many video cards are very integrated and have maybe one main GPU chip which you can't really replace (unless you're the company that makes such cards/chips, or unless you're a repair facility with access to spare parts or replacement cards).
Other than the main GPU chip there will be RAM chips which usually can be replaced if you're desperate for it, and various other things like capacitors / resistors which are easy for anyone to replace if it is easily determined they're broken to begin with.
Really ancient GPUs are made of less complicated and more standard chips, often a good number of them, instead of one main GPU and few other chips. These ancient cards are more easily repaired (if one can find the fault to begin with) at many different places.
Look for burn marks, obvious cracks, bulging / leaky capacitors, etc. and that'll give you an idea of what level of repair effort to investigate / hope for.