The two types of garden soil that really need to be amended the most are clay soil and sandy soil.
Clay needs to be amended to loosen it up. The roots of plants need to have the ability to transfer oxygen through the soil to the root system. That’s why plants do so well in loose soil.
The best way to amend clay is to work into the soil as much organic matter as possible. Rotted leaves, rotted grass clippings etc. It is ideal, if you have this material in a compost bin giving it a chance to break down before adding it to the soil, but not necessary.
Wood chips should only be added to soil after they’ve been sitting for at least 3 years, giving them a chance to break down before adding them to your soil. Fresh wood chips need a lot of nitrogen to decompose, and if in your garden they will pull that nitrogen from your existing soil, depriving your plants of the nitrogen that they need.
The more organic matter you add to your soil, the happier your plants are going to be. Do not remove soil from your beds before you start amending the soil. Doing so will create a “bathtub” where water can get into the bed, but will not be able to drain out. Not good for plants! Plants do not like “wet feet”. Just put the organic matter on top of the soil and mix it in by hand or with a tiller.
If you have really sandy or gravel based soil in your yard it’s a good idea to amend with organic matter just to add extra nutrition to your soil. Most plants actually love sandy or gravel soils, so you add organic matter to these soils to take a good soil to a superior soil that plants will thrive in.