One approach to figuring out what Jesus of Nazareth taught is to assume that the canonical Christian Gospels are infallible. Although the word ‘infallible’ covers a variety of views, the basic idea is this
If Jesus is depicted as saying something in a canonical Gospel, then he said that.
The questions on this approach mostly revolve around getting a proper translation and interpretation of what he meant.
This approach has strengths – it is fairly simple and gives us some fairly detailed ideas.
Often, people seem to argue that the primary weakness of this approach is of reconciling the different Gospel accounts, where it seems there are some discrepancies as far as the accounts that overlap. However, I don’t think this is an insuperable problem for an infallibilist – the inconsistencies are mostly minor details, involving supposed chronology, say. These can be explained as the result of copying errors, or by noting certain texts don’t say they are in exact chronological order, and so on.
Rather, the primary weakness of the infallibility approach is this. It’s not clear why one should assume infallibility, as one’s starting position, when it comes to these texts. The working position with regards to most any text isn’t to assume infallibility – one doesn’t do this anywhere else. If, after significant work on the texts, one comes to the conclusion that they’re completely correct, that’s different – but it should be borne of significant research, study, divine guidance, and so on. In short, it should be a conclusion, not a premise, just as the idea that these texts were inspired seems to have been a conclusion reached by the early Christians who put the canon together in the first place.
If you don’t start with an infallibility assumption, then what approach to understanding what Jesus taught makes sense? I think it is to look for larger trends of thought in the work.
What are some candidates? Jesus taught to focus on the inner spiritual life instead of the outer (prayer, for example, is about what you actually think and feel, not about being seen to be pious and uttering words in a rote manner). He taught a ‘dying to oneself’ in order to live in God (i.e., aligning one’s will with God’s, and then acting on God’s guidance). He taught loving one’s neighbour as oneself. He taught the attainment of inner peace (“Peace I leave with you, my peace I give unto you”). He taught the importance of a kind of ‘faith’ (active trusting) in achieving certain results (“Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them.”). He taught loving God with all one’s heart, mind, and strength. And so on.
The point is that broad trends can emerge. When you can see certain basic points of his thought, it also can make sense of passages that originally seem baffling.
If you are taking an infallibilist approach, then it’s easy to get tripped up by this line or that in the Gospel accounts. Taking an approach that looks for basic ideas, though, you can ask what teachings appear in multiple points, across texts, make sense of otherwise baffling sections, and so on, and then put them into practice to see if they actually work.