LTspice stands for Linear Technology's Simulation Program with Integrated Circuit Emphasis. It is a software suite for electrical simulations with schematic capture, an integrated waveform viewer, and supportive models to ease the simulation of analog circuits.
This is an overview of some of the capabilities of LTSpice from the website.
0:00 narrator begins by talking through some of the benefits of using LTSpice
1:39 narrator begins a demonstration of creating a schematic
4:20 narrator ends the demonstration and starts talking about useful tools on the website
Here is some documentation from the website and a 'getting started' guide
LTspice Information Flyer & Shortcuts (PDF)
Mac OS X Shortcuts (PDF)
LTspice Getting Started Guide (PDF)
The creators of LTSpice themselves do not have a basic video tutorial, so here is the start of a well reviewed tutorial series for absolute beginners
0:00 narrator talks about spice and how to acquire it
2:27 narrator finishes installation and begins tutorial the first tutorial is about basic element manipulation as you create a voltage divider.
The video description has links to the 27 other episodes of the tutorial, so if you are looking for help with something specific, you can check there