If you just bought it new and just got it installed and it crashes when you try almost anything then you might contact customer support directly. They are supposed to help with getting the program installed and running for you initially. This community is often aimed more at "how can I calculate this?"
It shows my age, but I would recommend you find an introductory book that seems to match your style and read that to help you get started. Mathematica Navigator is very old now, but has lots of simple examples on every topic. Used copies are sometimes only a dollar. That lacks some of the latest changes to Mathematica, but might help you understand the fundamentals.
= and == and := and there is even an === and those all mean totally different things to Mathematica. eq1 = x==y+f[z] roughly translates into english as "name the following thing eq1 and that thing is x==y+f[z] and that thing is comparing x with y+f[z] to see whether they are "equal" or not." When you type in that line and press <shift><enter> Mathematica will quietly remember that and if you later forget and try to use eq1 for something else you may be surprised.
Replacing one thing with another in Mathematica can be challenging, to put it politely. If you have a bright student and ask them to do a substitution in an equation they will use "mathematical maturity" or "common sense" to do that. Mathematica will often surprise you when you ask it to do the same. Exactly how it works is more than a paragraph is going to be able to explain.
Try this and see if you have any initial success
eq1 = x == y + f[z];
eq1 /. y -> g[z]
followed by shift and enter and see if it displays
x == f[z] + g[z]
Hopefully that will work for you. Note that has not changed the value you assigned to eq1. If you want to change the value then try
eq1 = eq1 /. y -> g[z]
and then check that the assignment worked by typing
eq1
I hope it works for you. Note: /. is one of many many Mathematica "shortcuts" that are often used instead of typing out the complete Mathematica function name. You can look up /. in the help system and see the examples there. You should be able to use ReplaceAll[eq1,y->g[z]] or the form I showed above and get the same result.
