Yesterday, in a Nahw class that I teach on Al-Tuhfa Al-Saniyya, I got into a discussion with students on how to read Arabic without harakat faster. The discussion resonated with a lot of the students, and I think that struggling to read Arabic quickly and properly is a very common thing that students of knowledge struggle with.
As a disclaimer, I'm not a perfect reader myself, and I have plenty to learn when it comes to Nahw and Arabic in general, but some of these tips might help you.
The assumption of this guide is that you have studied basic nahw like Al-Ajrumiyya already, and some basic Sarf. A lot of these insights were gained from books like 'Awamil al-Jurjani, some footnotes from Sh. Muhammad Muhyiddin's taqrir of Sharh Ibn Aqil, and other sources. I make some generalizations and over-simplifications in this guide, so keep that in mind as you are reading.
Only a Few Type of Words Are Mu'rab.
The reason why this tip is important is because reading with i'raab is mainly a process of elimination and eventually becomes an unconscious process. The original Arabs spoke naturally with i'raab without knowing a lick of Nahw, because in reality, declension is simple and only confined to a few types of words. If it was too complicated, it could not be a spoken language since it would require too much mental calculation. So the idea is that there's actually a lot of things that you don't have to worry about when reading Arabic.
Out of the three categories of words, huruf are all mabni. So reading huruf is easy because their endings never change. The default for af'aal is also that they're mabni- because a f'il madi and a fi'l amr are both mabni. Only the fi'l mudari' is mu'rab, so we only have to figure out the i'raab for the mudari', which we will come back to shortly. For asma', the default is that they are mu'rab, but there are a lot of asma' that are mabni like the dama'ir. But since the default is that they're mu'rab, so a lot of your brain power while reading and speaking is spent on doing their i'raab. However, the way to solve this is through understanding another basic principle:
The Default is Marfu
Now that we've narrowed the scope of i'raab to only be asmaa and the fi'l mudari', we should remember that the default of both of them is to be marfu'. If a sentence starts with a fi'l mudari', the default is that it is marfu'. Likewise for an jumla ismiyya- the mubtada is marfu'. So when we make a word majzum or mansub, it's actually an exception.
With this rule in mind, you've already narrowed the scope of i'raab to be even more. That means that you don't have to use any brain power to figure out if a word is marfu'- you only have to figure out if it's majzum, or mansub, or majrur. The next tip helps a lot with this.
The I'raab of Af'al Changes Due to Keywords (Huruf ul-Ma'ani) and The I'raab of Asmaa' [Usually] Changes Due to the Part of Speech
This idea is discussed/alluded to in books like Awamil Al-Jurjani, and once this clicked for me, I found this to be the missing link. Let me explain in more detail. Nouns and verbs change their i'raab due to the presence of modifiers ('awamil). These modifiers can be categorized into two: keywords (sama'i) and parts of speech (qiyasi).
Take the huruf ul-jazm as an example. They are a set of keywords: لم، ألم، ألمّا.... etc.. These keywords are grammatical agents that cause the fii'l mudari' to become majzum. Without these keywords, the fi'l mudari' remains marfu'.
On the other hand, look at what makes an ism mansub. It can become mansub because it is a maf'ul bihi, or because it's a haal, or because it's a dharf, etc.. In all of these examples, the ism is becoming mansub because it is playing a particular role in the sentence as the object of the sentence, the adverb, etc..
This simplifies doing I'raab because lists are very easy to remember. The i'raab of keywords is easy because you just need to memorize a few words. For the fi'l mudari', you just need to remember the words that make the fi'l mudar' mansub (it's really just 4 words- أن، لن، إذن، كي). Likewise, memorize the majzumaat. Once you know that, doing the i'raab of af'al will become second nature for you. Whenever you see one of the words that make a fi'l mansub or majzum, you can instinctively do the i'raab of the the fi'l that follows.
For asmaa', it's a bit more complicated, but you can simplify it even more. Asmaa become majrur in the same way- through these keywords: the huruf ul-jarr. Once you learn the huruf ul-jarr, you'll be able to consistently and easily know when to make an ism majrur. An ism is also made majrur through being a mudaaf ilayh, but those are quite easy to identify since usually the pattern of a mudaf+mudaf-ilayh is an ism without an alif-lam followed by an ism with an alif-laam.
Once you've learned the rules up to this point, you've actually mastered nearly everything you need. You now know how to do all the i'raab for words that are marfu' (since that's the default you'll read with), you also know the i'raab for when the fi'l mudari is mansub and majzum (by memorizing two lists), and you also know the i'raab for an ism when it's majrur.
That leaves one category:
Learn the Mansubaat of Asmaa'.
This is the last category left. Most of your brain power will likely go into figuring out when an ism is mansub while you're reading, because everything else is much simpler. For the asmaa', there are many different ways that it can become mansub, so that is where you should be spending most of your time. Learn how to identify the mansubaat and reliably apply them. One good thing is that most modern prints of books, even the ones that have very little tashkil, know that identifying an ism to be mansub is hard, so they'll sometimes write the tashkil for these words, so that your reading is smoother. The better you get at this, the better your i'raab will become.
To conclude, this should help with ~80% of your reading. The other 20% will come from general knowledge of Sarf and the fine details of Nahw, practice reading out loud, and increasing one's vocabulary and understanding of Arabic in general. I should also add that working on one's tajwid and consistently reading Qur'an helps tremendously as well. Of course, the list of tips that I gave is not exhaustive, so if you have more tips, definitely share them.