Recently, I am working on writing a review about a book and I wanted to know how I can check my grammer mistakes. In other words: how can I write a paragraph or essay in a right way without any grammar or spelling mistakes? And if there are any resources I can learn from, please let me know.
You can't be one hundred percent sure that you don't have any mistakes in your writing. It's the same as with testing a program - you can find bugs and be certain that a version therefore has flaws, but there will almost always be things you just can't test, because you don't have the time to fully check every little detail in a project of a significant size.
There are many tools that can help you, such as the basic spellcheckers that programs like Microsoft Word have already included. They will be able to pick up a lot of common mistakes and make you aware of them. But there will always be edge cases where these spellcheckers are simply wrong. See Knowing when to disobey the advice of grammar software for more information about this topic.
You can also give your draft to someone that regularly checks writing for mistakes. Professional editors can help you a lot. See Where do I go looking for an editor? and How do I find an affordable editor? for more information.
You can also write something and then let it sit for a couple of days or weeks while working on something different. You will more easily pick up the problems in your writing if you are not so close to your writing anymore, because you are routine-blinded when reading the same thing over and over. See for example this answer to So I finished my novel. Now what do I do? for more information. This advice works better if it's a longer project that you are working on where you can simply take a few days off.
For a general tips collection on making fewer mistakes (as opposed to none that you are aiming for) you might want to look at How can I catch more errors when I proofread?