The most important thing is having the right blade and it should be sharp. If the blade has been used for a while, it can help to clean off any buildup of gum and pitch. You want the exposed face up or down as needed depending on the saw you are using. Also depends on the wood species and direction of the grain. Sometimes it's necessary to experiment with 2 or 3 blades to find the best one.
Depending on your installation detail, maybe you can round over exposed edges by hand or with a router.
Painter's tape can help. Sometimes you can clamp a scrap piece of wood for backup against your finish piece to prevent tearaway. Another thing you can try is scoring the wood with a
sharp utility knife first. This can work surprisingly well once you've got the hang of it. A really nice clean cut can be made with a thin-bladed flexible hand saw like a Japanese carpenter's saw or flush cut saw as in the photos which have a high tpi. You would clamp a piece of wood to your work piece and hold the blade against it while cutting. I've had one of the 2-sided ones for a long time and has been really handy for a lot of misc. things.
Be thankful it's not the vinyl/paper wrapped faux wood they use in RVs. I special ordered a couple of 8' lengths of 1x2 from our dealer for some cabinetry work in our TT and found that the stuff is a real b**ch to cut cleanly. I have a chop saw but didn't want to chance it and had my next neighbor, a cabinet maker cut it for me and even he had trouble and after trying several blades. Can't even sand the cuts to clean them up.
FWIW, even after years of college, the most useful and enjoyable classes I have EVER taken, bar none, are woodworking 11 & 12 in high school decades ago... :)