First of all, we need to prepare the song. It has to be in the MP3 format, and the sampling rate should be set to 44.1 KHz (you can change it using Audacity, if you have a problem with that). For example, if you want to replace the song "Apprehension and Evasion" with the song "Klaxon Beat", copy the replacment from the HL1 files (the name is Half-Life12), but if you don't have HL1, you can download the soundtrack from internet. (for example: https://downloads.khinsider.com/game-soundtracks/album/half-life-original-soundtrack) After getting the song, rename it to the filename of the song you want to replace (for example, "HL2_song29").

Go to your Steam folder, then "steamapps" folder, "common", then your Half-Life 2 folder, and to folder named "hl2". Here, create a folder named "custom", in it create another folder named "root", then in folder "root" create a folder named "sound", and finally in the folder named "sound" create a folder named "music".
After that, your file path to folder with music should look like this:
<folder where you have Steam installed>\steamapps\common\Half-Life 2\hl2\custom\root\sound\music.
After creating the folders, put your custom "HL2_song29" (or other music files you want to replace) in the "music" folder.

After that, launch Half-Life 2 and enjoy your custom music!
Note that this method will work with HL2 episodes, you just need to create "custom" folder either in "episodic" folder or in "ep2" folder.

Special thanks to @DahMainahGaimah for the instructions!