Overview

If you really ever tried to improve at Dota2 aside from spamming <enter hero name here>, you for sure could find your improvement rate significantly stagnate at some point. At this time you really have to discover new ways of pushing your progress, not just blindly play more. This guide serves as one of such ways.
So what is it all about? Remember countless times when you chased a hero down the lane on your Juggernaut, and finally got in range to cast your Omnislash – all just to hit your target one time and jump to the creep wave right behind them. Or maybe you saw a 100 hp hero fleeing from a teamfight, your fingers already started smashing "EEE" getting ready for that sweet, sweet sunstrike (I know you are there, pesky Invoker pickers). You are so good you predicted their movement pattern and got'em! And other 4 creeps aand a carty as well. So, you get the idea. It may actually take some effort (wow) to master this principle of knowing where exactly are enemy creeps at any point in time. But stick with me, and I'll show how to make it efficiently (kinda). Results are definitely rewarding, as it is useful in maany situations (planning tier-1 dives, improving your farming patterns (both in efficiency and safety), predicting where those BoT Tinkers/Invokers going to TP, syncing your Overwhelming Odds and Berserker's Call to hit more units, etc. etc.).

Timings

Our ultimate goal is to keep in head some numbers, and occasionally try to get any use of them. These are the numbers – green timings indicate pathing of Radiant creepwaves, and yellow indicate Dire creepwaves. Each of the timings is defined as the moment when the leading creep in the wave goes past the point. In other words, it is approximately when "the center" of the wave reaches the point, at least before 46:00 minute mark.

Nuances

You're probably asking me: Ok, I learn all this shit from imgur link and I'm done yes? 5k awaits? The answer is no. Dota sometimes is ridiculously complicated, and this case is not an exception. The thing is, at 16:00 and 31:00 (I know it says 15 and 30 on wiki page, but it's not true) an extra melee creep is added to each creepwave, and at 46:00 an extra melee+range creeps are added. As a result, creepwaves get longer and clunkier. BUT it doesn't influence the timings as much as the fact that with addition of extra creeps to the waves, creeps simply start to spawn later. Just consider these two screenshots, which show creeps spawning at 0:00 and at 46:00 min marks. Because of this mystical delayed spawn timers, we should adjust timings accordingly. Also remember that before 7:30 safelane creeps are uber-fast and offlane creeps are uber-slow. But for some reason Radiant safelane creeps retain their uber-speed until they reach T2, and Dire offlane creeps cosplay snails all the way down T1. Compare this to creeps on the other lane, which retain their speed adjustments for about whole 2 seconds! To sum up, adjustment rules go as follows:

• Before 7:30 substract 2 sec from all Radiant safelane timings
• Before 7:30 add 5 sec to all Dire offlane timings
• After 16:00 add 1 sec to all Midlane timings
• After 31:00 add 1 sec to all Safelane and Offlane timings (both Radiant and Dire)

Note that we don't adjust timings according to siege creeps (each 7^th wave starting at 3:00), because they don't really influence timings. As I said, it is delayed creep spawn timers that have an impact.

Actual Guide

As promised, I provide an effective and fast way to learn the timings. Of course, you could go and just learn them straight away, like as you did with multiplication table in elementary school, but I get a feeling it won't help you much if you just "know the math".
We will try to learn "by practice". What it means, we will create a lobby and artificially make an environment where we will be able to effortlessly test our timing knowledge. You don't really need to remember them by heart. All you need is just a bit of repeated practice, and then applying what you have learnt in real games.

1. Go into a private lobby with cheats enabled, AP mode
2. Pick Axe, -lvlup 24, -gold 100000, -wtf. Buy a Blink Dagger and some Hearts (-item item_heart).
3. What we do next may seem a bit gimmicky but it is essential (please let me know if there is a better way to do it). Type -allvision. Then put your cursor in the middle of your T3 ramps and type -createhero bristle, after that turn him so he faces fountain (just like this). Do the same for your midlane and top lane.
4. Create 3 enemy Bristlebacks with -createhero bristle enemy at enemy mid, top and bot tier-1s.
5. Type -levelbots 24, -givebots item_heartx6
6. Send enemy Bristlebacks down the lanes, so they destroy all your T1, T2 and T3s. In the end, put them just in front of the racks facing your frienly Bristlebacks (like this)
7. Select all Bristlebacks one by one and level up Quill Spray (4 points) and Bristleback (1 point is enough)
8. What we got in the end? Live walls meant to be keeping all the lanes pushed to your base ramps at all times, yet preserving the racks.

Now you are finally able to get into the action! Turn your maphack off with -normalvision. Go to the lanes, hide behind the trees where you have no vision of the lane, and start jumping out and using your Berserker's Call like a true ninja. If you manage to call all (or most) the creeps from the wave, you are doing it right. Do a round of jumps to enemy tier-2s, then tier-1s, then slowly progress to your side of the map. Find out what exact points other timings (not in circles) represent, get a feel of them – this is your homework. Maybe even adjust some of them if you wish so. Try practicing before 7:30, after 16:00 and 31:00 and see the difference. Have some fun, would you?

TL;DR

Here you can see the timings when creepwaves pass certain points on the map. You can use these timings in various situations (e.g. making sure to hit a sunstrike when there are no creeps). Adjust timings as said in unordered list from Nuances section. You can practice timings in a private lobby, trying to predict where creeps go at any given point of time.

p.s. To go along the rules, excuse my poor englando (am russian from China). And this is my first post on Reddit, so yeah, hope it's helpful.