First you'll need to know if you're capable of making a Let's Play. Let's Plays are usually highly entertaining beyond simply playing the game. This commonly takes the form of having a running commentary that's either informative and/or funny. In order to retain the attention of a viewer, you should be capable of delivering such an experience. This also might require excising your voice if you're not used to talking at length.
Second, means of recording and editing the game footage. In order to capture console footage, you'll need a Video Capture card, as well as a video capture-capable program (commonly built into newer Video Editing suites). In order to retain high quality for the capture, do proper research for what kind of card you'll need, in addition to supplemental hardware to ensure it works to the best capability. (Extra RAM, more powerful processor, larger power supply, Etc.)
In addition to the card, you'll need a cable which can connect the Card input to your TV's output. What kind of cable may be dependent on what kind of TV you have, and it's output. (Standard Definition? 720p HD? 1080p HD? Framerate PAL, NTSC-non-drop, NTSC-drop?)
Once you have your video recording set up, editing should be relatively straightforward unless you plan on having fancy title sequences or audio formatting, which would require you looking into tutorials on how to do that with your Video Editing program.
Hope it helps!
However, if you planned on starting it up just for fun, I'll explain it in short terms: there is no way of capturing Console video game footage into a computer video format for free. You will need some form of connectivity between your console and computer via TV and/or video camera conversion.