How do I use the step and ramp functions to create a specific signal?
You have a confilct in your definition for t &lt; 0.

I'm going to assume you mean f(t) = 0 for t &lt; -1, with the rest of the definition unchanged. 

The simplest way I can think of doing this is to use u(t) as a tool to switch functions on and off over the desired ranges of time.  For example, if you want a function to be on over a range of time, say t1 to t2, multply the function by u(t-t1)-u(t-t2).  This turns the function on at t1 and off again at t2.

One representation of your function is:

$$f(t) = [u(t+1)-u(t-1)]t + 2u(t-1)$$

For this representation, we've used two functions: t and the constant function 2.
The function t is switch on at t1=-1 and off at t2=1.  The constant function '2' is switched on at t2=1 and never switched off.

If you need to use the ramp function instead of t, your function is:

$$f(t) = -[u(t+1)-u(t)]r(-t) + [u(t)-u(t-1)]r(t) + 2u(t-1)$$

Here we've used three functions: -r(-t), r(t) and 2.