Most Russian consonants come in pairs. One is soft (also called palatalized) while the other is hard (non-palatalized). For English speakers the easy way to think about this is to think of most Russian consonants having two versions (two versions of "L", "T", etc).
So what exactly is the difference between hard and soft consonants? It all comes down to the sounds they make and how those sounds are produced in the human mouth.
As we mentioned before, soft and hard consonants are also known as palatalized and non-palatalized consonants. This term palatalized comes from the word palate, which is literally the top of your mouth.
In Russian soft consonants involve touching a part of your tongue against the top of your mouth (palate), while hard consonants usually do not.
For a further break down of palatalization, consonant pairs, and correct pronunciation check out the video below:
A closer look: Russian Consonants and how to pronounce them
Notable exceptions
3 consonants that are always hard
There are three Russian consonants that are always hard (that is they have no soft counterpart) and are never soft. They are: ж, ш, and ц.
3 consonants that are always soft
There are three Russian consonants that are always soft (they have no hard counterpart). They are: ч, щ, and й.
How to tell whether a consonant is soft or hard
Look out for the ь
The sign "ь" called Мягкий знак (or simply soft sign) often shows up in Russian words (most commonly at the end). It has no sound of its own. It simply shows that the consonant that comes before it is pronounced as a soft palatalized consonant. Here are two common examples:
мать (mother)
свадьба (wedding)
The ь is used when a soft consonant comes at the end of a work, or if the soft consonant comes before another consonant.
Look out for soft sign vowel letters
There are five Russian vowels that indicate that the preceding consonant is soft: я, ё, ю, е, and и. Anytime you see these vowels after a consonant it means that the consonant is pronounced as a soft consonant.
Application
Given what we know about the soft sign and soft sign vowels, let's take a look at a couple Russian words and try to determine which consonants are pronounced as soft and which are pronounces as hard.
Our first example is the Russian word for mirror:
зеркало
In this word there are four consonants: з, р, к, and л. Of these four only з is pronounced as a soft consonant because it is the only consonant in the word that is followed by a soft sign vowel (in this case the letter е).
Let's take a look at a word from one of our earlier examples:
свадьба
In this case the д would be pronounced as a soft consonant because it is followed by the soft sign (ь).
Conclusion
The Russian sound system takes some time to adjust to. Luckily though, the rules are fairly logical and consistent. Once you get used to them you won't even think about whether a particular consonant is hard or soft. With a bit of practice it all starts to feel like second nature.