It sounds like you're asking:
How do I know reality is real?
So, there are variety of scenarios that have been offered in philosophy that challenge the thinker to think about proof and reality. All of them center around how do you prove reality is real:
This is a good introduction into some key philosophical terms that stem from asking some simple-sounding questions:
- What is reality?
- How do I know what is real?
- How do I prove something is real?
- What is evidence?
These are the sorts of questions that start one down the path of reading more complex philosophy! Let's just craft a simple response. By knowing the four definitions above and then being acquainted with some key ides, you can begin to answer the question for yourself.
Ontology
The study of reality and its substituents is called ontology. The starting position of many thinkers about how build up the picture of reality and figuring out which things are part of it is that of naive realism. As a thinker becomes more sophisticated they might find other models such as scientific realism or subjective idealism, and so on. In the West, educated society has largely moved towards philosophies that are grounded in naturalism and physicalism in the secular world though Christian theology is still a fundamentally powerful source of philosophical thinking. Modern Catholicism offers a good blend of both.
Epistemology
How do you know something is real? How do you know anything and what is knowledge? The classical tradition going back to the Socratics is that of justified, true belief. There are some technical problems arising from Gettier problems. Then there are sources. Robert Audi, for instance, offers consciousness, reason, testimony, perception, and memory. The technical language about deciding whether something exists has to do with terms like existential quantification and quantifier variance, but those tend to be ontological terms where as the actual justification or judgement (SEP) is rooted in philosophy in terms of argumentation theory.
Proof and Evidence
These two terms are highly interlinked. A proof is a method that uses evidence to justify a conclusion. This requires a theory of evidentialism. This will vary from thinker to thinker. For instance, it is quite typical for theologians to accept supernaturalism and the power of faith. Revelation features quite prominently in terms of evidence among some traditions. In the secular world, empirical evidence and rationality figure quite prominently in proof. A good place to start for informal reasoning is Toulmin's Uses of Argument for his method. Argument maps are another tool for organizing proof and evidence.
The Non-Answer to Your Question
What you accept as proof that reality is real will be up to you. There is no authority that can tell you what is right and wrong, though some ideas and techniques are more useful than others. That means you'll have to read through these sorts of materials and come to a decision about what you personally favor. Personally, I would appeal to James Halliday aka Anorak the All-Knowing:
And that was when I realized that... as terrifying and painful as reality can be, it's also... the only place that... you can get a decent meal. Because, reality... is real.