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.

I realize there is the old way of doing things, that was back when people like me were desperately working with mud trying to invent the stone so we could celebrate entering the stone age and sheets of paper glued into piles was how information was kept together, and there is the new way of doing things, where information is communicated directly to your brain using holograms and smell alone. If you have to go looking for a video then I wish you luck, but you didn't seem to indicate that you had had any luck with the new ways.

New purchase, new install, continual crashing so contact customer support directly and see if they can help you get that solved.

When you have really understood substitutions and can effectively use those within Mathematica then you might find that it can be easier, faster and less error prone than cut and paste with your mouse. You can name very large things and refer to them just by their name.

Perhaps depending on which version you have you may see Evaluation on the menu bar at the top of your window. You can click on that and then see the drop down menu listing Quit Kernel. Clicking on that and then on Local and then on Quit will tell Mathematica to discard all previous stored results. The calculations displayed in the screen will still be there, but any stored values from your previous calculations will be lost. And clicking on Evaluation and then Evaluate Notebook will step by step do every single step in your notebook. To tell Mathematica to "forget" the stored value of eq1 try this

eq1=.

What is written in the notebook can be very different from what Mathematica has been previously told to store in memory. This often causes confusion for new users.

Everything I have written here and thousands more things will be described in some online video somewhere. Maybe try Google with

Mathematica video introduction

and see if you can find something. That seems like what I would have tried.

Lastly I will say, there is the "Mathematica way of thinking" and until you have come to understand some of that you may find Mathematica to be confusing and aggravating. After you have learned some of that then it may be confusing and aggravating, but for much higher reasons. And repeat. And repeat.

I hope it works out for you. I'd start by contacting customer support until you get the crash problem fixed.

http://www.wolfram.com/training/courses/mathematica/ lists free and for-pay videos.

Introductory pages in the online/in-product documentation are not as obvious as they used to be. I suggest starting with Help menu - Wolfram Documentation or http://reference.wolfram.com/language/ and starting at the beginning with Core Language & Structure.

Pick a sub-topic, for example, Language Overview, click it, and in the upper-right corner choose a tutorial.