Try looking on google.co.uk and entering 'English sentence patterns' - I found lots of sites that should be of help. Some of them have online exercises as well.
There are many different terms used, but basically they mean subject (the active person or thing in the sentence), verb (the action that is being carried out) and object (the person or thing that the verb is acting upon). For example, Jane (suject) ate (verb) the cake (object). The subject-verb-object pattern is one of the most basic sentence patterns in English.
I'm not too sure what is meant by 'linking verbs', but 'transitive verbs' are verbs that require an object - I prefer coffee - you cannot say 'I prefer'.
Hope this is of help,
- For Teachers