Fingering is one of those weird things in so far as sometimes it matters and sometimes it doesn’t matter at all. Talk about being confusing.
Whenever there is fingering put on a page of music, it has been put there for a reason – to make sure that the correct finger is used so as to facilitate the flow of the music. Ususally the person who has put the fingering in, is someone that is used to editing music and usually has a thorough understanding of the music. While this is true most of the time, it is not true all of the time. I have and do come across fingering on a semi regular basis that I completely disagree with and when I disagree with fingering, I just simply change it.
In my opinion, it is always best practice to use the fingering that is marked and just in case it has never been explained, the thumbs are labelled as 1 , index fingers are 2, middle fingers are 3, ring fingers are 4 and little fingers are 5.
The goal of fingering is not to be flamboyant or fancy, the goal is to facilitate the flow of the music as much as possible, so you can’t hear when your hand needs to move, but rather you just don’t even think about it when you are listening.
So here’s what to do when you don’t have any fingering marked. Always look for an obvious fingering – sometimes it will be really obvious and sometimes it will be next to impossible. Try to use all of your fingers when appropriate, rather than just two or three on each hand – you will get a superior sound when you do. Try to avoid using your thumbs on a black note where possible. Sometimes it will literally be too uncomfortable to play the notes if you don’t use your thumbs. Remember your goal is to have the music sound at its best and a poor choice in fingering can really hinder that.
What you also have to take into consideration is that if the fingering that you have chosen, or it is written on your music and it causes pain in your fingers, hands or wrists, then you must adjust and adapt the fingering so you are no longer in pain. Remember that discomfort for a moment with a few notes is not the same thing as pain. Pain is unaccepteble and fingering has to then be adjusted.
The purpose of fingering is to make the music sound as best as possible, while making it as easy as possible for the person playing the notes to reach them and articulate the notes in the way it was intended. If the fingering is terrible, either the music will not sound as good as what it can or the person playing will get sore hands or fingers. Neither of these two things are a good outcome, so please give due consideration to your fingering.