Originally, texture similar to drywall trowel texture were found in plastered homes. However, drywall compound has been used to achieve the same appearance. It will take more practice and experimenting to match this type of texture. The first thing to do is determine if anything has been added to the mud, such as sand.
Not sure if this is the right texture? See the article 'Types of Drywall Texture' for more information on all the texture types. Need to patch some drywall? See the article 'How To Patch Drywall' for instructions.
Generally a drywall trowel texture will be done with a fairly stiff mud. You apply the mud with a trowel and then use the trowel to achieve the pattern. Spanish textures are globs of mud flattened out. The trowel is often 'hooked' at the end of the stroke to give it a look (experiment, remember?). Fans, circles and other patterns are done by applying the compound in the desired pattern.
There are many, many variations and you will have to keep trying until you get something that works. This is definitely not an exact science. Even if you call a professional, they will need to experiment to get the right look. Trowel texturing drywall or imitating plaster textures is more difficult. Hopefully you were able to get something you are happy with.