My question is not about depth, but area. For a given individual plant, do I amend the soil for an area the size of its seed spacing recommendation (12 in., etc.)? Or is less required? I am a complete beginner. Thanks!
The best is to prepare an entire area thoroughly before planting by digging it all over properly, incorporating organic composts if you feel its appropriate for whatever you're growing. That might mean a whole planting bed, or a border, but its best to dig it all first, let it settle for a week or so, then its all ready to plant, rather than 'spot' digging where you want plants to grow. Only digging small parts means the plants may be restricted by compacted or unamended soil surrounding where you've dug - plant roots want to go where the nutrients and water are, and that's often hard to predict, especially with larger plants.