Changing the oil of a Honda CBR125R is a very simple operation, it requires just few tools, a bit of time (10-15 minutes), and limited mechanical skills. Before performing this procedure, the engine (and so, the engine oil) should be hot enough, so that the oil viscosity is low and the oil can flow out easily; for these reasons, I recommend you to ride your motorcycle for 5-10 minutes before performing the following oil change procedure.
First of all, you need to remove the fairings of your motorcycle. The screws positions are symmetric, so I will show you how to remove just the right side of your fairings, and the left side will be the same. In order to perform this procedure, you need an hexagonal key. Start by removing the following screw (first).
Then, remove the next screw (second).
And then, remove the last screw (third). After removing this screw, you can remove the right side of the fairings. Perform the same steps also for the left side of the motorcycle.
Remove the following screws, both on right and left sides of the motorcycle.
Remove the oil drain bolt (you need an hexagonal wrench), on the lower side of the engine crankcase. Please note that, just by removing this bolt, the oil will not start to flow out. You will need to remove also the black cap (following step), so that the air can flow into the crankcase.
Remove the black cap on the oil filling hole. When you loose this black cap, the oil will start to flow out quickly, so prepare in advance something under your motorcycle, to collect the used old oil.
The black cap and the oil drain bolt are as following. Please note that the drain bolt in the picture is an SP Takegawa aftermarket bolt (SP武川 アルミドレンボルト M12X1.5 シルバー 02-09-0002) which I bought on Amazon Japan for ￥1,404 (10 Euro); it has a magnet which helps to collect the "metallic garbage" created into the engine due to the friction.
After draining the engine oil, you can mount again the drain bolt, but before doing it, you should change the washer to a new one. The correct product is (STRAIGHT/ストレート) ドレンパッキン バイク用 M12×20mm×2.0T 19-81912. I bought the following from Tool Company Straight, on Amazon Japan, for few Euros; you will need only one each time you change the engine oil. I suggest you to fix the bolt with a moderate torque, but do not put too much force, because you may damage the crank case.
As new engine oil, I chose the MOTUL(モチュール)5100 4T 10W30 バイク用化学合成オイル 1L[正規品] 11204411, bought on Amazon Japan for ￥2,214 (15 Euro). I definitely recommend you to choose a good engine oil for your motorcycle. Since the Honda CBR125R requires only 1 liter of engine oil, there is not much difference, in terms of money, between choosing a cheap oil and an expensive oil. But in case you buy a good engine oil, such as the one that I bought, you will notice that the performance of your motorcycle will increase a bit, due to the lower frictions inside the engine. And also, the fuel economy will improve. Last but not least, I noticed that after changing to this good engine oil, the gear shifting became smoother than before. So, I definitely recommend it.
After putting the new oil, put the oil black cap on the hole, and verify that the oil quantity is enough (on the black cap, there is an arrow for that purpose). Also, check that there is no oil leakage from the lower part of the engine crank case. In case of no problem, start the engine, go for a ride, and check again that there is no leakage. If everything is fine, your job is finished, and you can enjoy the motorcycle.