Command line
Synopsis (from a terminal command line):

pdflatex options argument

Run LaTeX on argument. In place of pdflatex you can also use xelatex, or lualatex, or dviluatex, or latex.
For example, this will run LaTeX on the file thesis.tex, creating the output thesis.pdf.

pdflatex thesis

Note that .tex is the default file extension.
pdfTeX is a development of the original TeX program, as are XeTeX and LuaTeX (see TeX engines). They are completely backward compatible. But the original program had a custom output format, DVI, while the newer ones can output directly to PDF. This allows them to take advantage of the extra features in PDF such as hyperlinks, support for modern image formats such as JPG and PNG, and ubiquitous viewing programs. In short, if you run pdflatex or xelatex or lualatex then you will by default get PDF and have access to all its modern features. If you run latex, or dvilualatex, then you will get DVI. The description here assumes pdfLaTeX.
See Command line options, for a selection of the most useful command line options. As to argument, the usual case is that it does not begin with a backslash, so the system takes it to be the name of a file and it compiles that file. If argument begins with a backslash then the system will interpret it as a line of LaTeX input, which can be used for special effects (see Command line input).
If you gave no arguments or options then pdflatex prompts for input from the terminal. You can escape from this by entering <control>-D.
If LaTeX finds an error in your document then by default it stops and asks you about it. See Recovering from errors for an outline of what to do.

Command line options
These are the command-line options relevant to ordinary document authoring. For a full list, try running ‘latex --help’ from the command line.
With many implementations you can specify command line options by prefixing them with ‘-’ or ‘--’. This is the case for both TeX Live (and MacTeX) and MiKTeX. We will use both conventions interchangeably.
-version 	Show the current version, like ‘pdfTeX 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian)’ along with a small amount of additional information, and exit.
-help 	Give a brief usage message that is useful as a prompt and exit.
-interaction=mode 	TeX compiles a document in one of four interaction modes: batchmode, nonstopmode, scrollmode, errorstopmode. In errorstop mode (the default), TeX stops at each error and asks for user intervention. In batch mode it prints nothing on the terminal, errors are scrolled as if the user hit <return> at every error, and missing files cause the job to abort. In nonstop mode, diagnostic message appear on the terminal but as in batch mode there is no user interaction. In scroll mode, TeX only stops for missing files or keyboard input.
For instance, starting LaTeX with this command line

pdflatex -interaction=batchmode filename

eliminates most terminal output.
-jobname=string 	Set the value of TeX’s jobname to the string. The log file and output file will then be named string.log and string.pdf.
When you run pdflatex options argument, if argument does not start with a backslash then TeX considers it the name of a file to input. Otherwise it waits for the first \input instruction and the name of the input file will be the job name. This is used to name the log file the output file. The jobname option overrides that process and directly specifies the name. See Command line input for an example of its use.
-output-directory=directory 	Write files in the directory directory. It must already exist.
--shell-escape 	--no-shell-escape 	--enable-write18 	--disable-write18 	Enable or disable \write18{shell command}. The first two options are for with TeX Live or MacTeX while the second two are for MiKTeX.
Sometimes you want to run external system commands from inside a LaTeX file. For instance the package sagetex allows you to have the mathematics software system Sage do calculations or draw graphs and then incorporate that output in your document. For this TeX provides the \write18 command.
But with this functionality enabled, security issues could happen if you compiled a LaTeX file from the Internet. By default \write18 is disabled. (More precisely, by default TeX Live, MacTeX, and MiKTeX only allow the execution of a limited number of TeX-related programs, which they distribute.)
If you invoke LaTeX with the option no-shell-escape, and in your document you call \write18{ls -l}, then you do not get an error but the log file says ‘runsystem(ls -l)...disabled’.
-halt-on-error 	Stop processing at the first error.
-file-line-error
-no-file-line-error 	Enable or disable filename:lineno:error-style error messages. These are only available with TeX Live or MacTeX.

Command line input
As part of the command line invocation pdflatex options argument you can specify arbitrary LaTeX input by starting argument with a backslash. This allows you to do some special effects.
For example, this file (which uses the hyperref package for hyperlinks) can produce two kinds of output, one for paper and one for a PDF.

\ifdefined\paperversion        % in preamble
\newcommand{\urlcolor}{black}
\else
\newcommand{\urlcolor}{blue}
\fi
\usepackage[colorlinks=true,urlcolor=\urlcolor]{hyperref}
  ...
\href{https://www.ctan.org}{CTAN}  % in body
  ...

Compiling this document book.tex with the command line pdflatex book will give the ‘CTAN’ link in blue. But compiling it with pdflatex "\def\paperversion{}\input book.tex" has the link in black. (Note the use of double quotes to prevent interpretation of the symbols by the command line shell; your system may do this differently.)
In a similar way, from the single file main.tex you can compile two different versions.

pdflatex -jobname=students "\def\student{}\input{main}"
pdflatex -jobname=teachers "\def\teachers{}\input{main}"

The jobname option is there because otherwise both files would be called main.pdf and the second would overwrite the first.
A final example. This loads the package graphicx with the option draft

pdflatex -jobname=aa "\RequirePackage[draft]{graphicx}\input{aa.tex}"

so the graphic files are read for their size information but not incorporated into the PDF. (The jobname option is there because otherwise the output file would be graphicx.pdf, as \RequirePackage does an \input of its own.)

Recovering from errors
If LaTeX finds an error in your document then it gives you an error message and prompts you with a question mark, ?. For instance, running LaTeX on this file

\newcommand{\NP}{\ensuremath{\textbf{NP}}}
The \PN{} problem is a million dollar one.

causes it show this, and wait for input.

! Undefined control sequence.
l.5 The \PN
           {} problem is a million dollar one.
?

The simplest thing is to enter ‘x’ and <return> and fix the typo. You could instead enter ‘?’ and <return> to see other options.
There are two other error scenarios. The first is that you forgot to include the \end{document} or misspelled it. In this case LaTeX gives you a ‘*’ prompt. You can get back to the command line by typing \stop and <return>.
The last scenario is that you mistyped the file name. For instance, instead of pdflatex test you might type pdflatex tste.

! I can't find file `tste'.
<*> tste
        
(Press Enter to retry, or Control-D to exit)
Please type another input file name:

The simplest thing is to enter <Control> and ‘d’ (holding them down at the same time), and then retype the correct command line.