Well, first off let's address the immediate question.
'node *' is how you will declare a variable that is a pointer to a node.
Pointers are really hard, so you'll have to spend a bit of time to understand it, but when you create a pointer, what fills in that variable are (in my understanding) characters which make up an address. When you use malloc, what malloc returns are characters to an address. So a line like:
node * example = malloc(sizeof(node));
first declares a variable, example, which is of type 'pointer to a node', and then assigns it (ie makes it equal to) an address returned by malloc. Malloc will create a chunk of memory to the size of node.
So now in memory you have
example: 123fakestreet - the address will actually look something like 0x633000 but don't worry about it.
Then if you go to
123fakestreet: memory with null / garbage data that is the size of a node.
Now let's talk about * node - you can't really * a node itself - * 'dereferences' a pointer which means it goes to the address and sees what is there. So the thing you have to put after a * has to be a pointer in this instance. I'm not sure what will happen if you don't - probably a segfault or an error.
When you dereference the pointer you would write it as:
*example.field = 5;
the *example part essentially tells the computer to go into the memory at the address pointed to by example (remember, the 'example' variable itself is ONLY the address itself). Because nodes are structs, I've arbitrarily assigned a 'field' to it, which could be anything but I've made it an int.
So basically star in front dereferences and must be used with a pointer.
In terms of how to start PSET5, it's not easy - you'll spend a lot of time wrestling with it - it's much harder online given that it can take hours / days to get basic questions answered.
The best advice I can give (not having finished it myself) is to keep going, keep reading stack, keep asking questions and watch the overviews / videos a few times. The concepts take a while to build.
I'd also suggest reading and going through the examples on LinkedLists described in the course: http://cslibrary.stanford.edu/103/LinkedListBasics.pdf