Being new to this field, I've read quite about Critical Path and now understand its important to closing a project on time and on budget. I don't have MS Project, so as an alternative, what's a solid software program to do the job of providing information on the Critical Path and give the ability to plot out Gantt charts? Please explain the steps to help ensure the project is on time/budget and how to plot the Gantt chart.
There are several questions here each looking for a simple answer that I don't think exists.
At the end of the day you can develop a schedule and identify the critical path using paper and pencil if you have to. Software isn't going to help you in the long run, but understanding what the software is doing for you will. If you are a new PM and have a simple project I advise you to do this first so that you will understand the underlying logic. Wikipedia is as good a place as any to start learning what a critical path is.
Same for ensuring a project is on time/budget. No simple answers and, unfortunately, a huge amount of the learning will be experiential (i.e. on-the-job). At a high level keeping a project "on track" involves a lot of effort in:
All of these have tools that vendors will try to sell you, but at the end of the day it will be your experience and ability to use your soft skills to herd a pack of cats in generally one direction that will make or break a project.