How do I grep for multiple patterns with pattern having a pipe character?

First, you need to protect the pattern from expansion by the shell. The easiest way to do that is to put single quotes around it. Single quotes prevent expansion of anything between them (including backslashes); the only thing you can't do then is have single quotes in the pattern.

grep -- 'foo*' *.txt

(also note the -- end-of-option-marker to stop some grep implementations including GNU grep from treating a file called -foo-.txt for instance (that would be expanded by the shell from *.txt) to be taken as an option (even though it follows a non-option argument here)).

If you do need a single quote, you can write it as '\'' (end string literal, literal quote, open string literal).

grep -- 'foo*'\''bar' *.txt

Second, grep supports at least¹ two syntaxes for patterns. The old, default syntax (basic regular expressions) doesn't support the alternation (|) operator, though some versions have it as an extension, but written with a backslash.

grep -- 'foo\|bar' *.txt

The portable way is to use the newer syntax, extended regular expressions. You need to pass the -E option to grep to select it (formerly that was done with the egrep separate command²)

grep -E -- 'foo|bar' *.txt

Another possibility when you're just looking for any of several patterns (as opposed to building a complex pattern using disjunction) is to pass multiple patterns to grep. You can do this by preceding each pattern with the -e option.

grep -e foo -e bar -- *.txt

Or put patterns on several lines:

grep -- 'foo
bar' *.txt

Or store those patterns in a file, one per line and run

grep -f that-file -- *.txt

Note that if *.txt expands to a single file, grep won't prefix matching lines with its name like it does when there are more than one file. To work around that, with some grep implementations like GNU grep, you can use the -H option, or with any implementation, you can pass /dev/null as an extra argument.

---

^{¹ some grep implementations support even more like perl-compatible ones with -P, or augmented ones with -X, -K for ksh wildcards...}

^{² while egrep has been deprecated by POSIX and is sometimes no longer found on some systems, on some other systems like Solaris when the POSIX or GNU utilities have not been installed, then egrep is your only option as its /bin/grep supports none of -e, -f, -E, \| or multi-line patterns}

egrep "foo|bar" *.txt

or

grep "foo\|bar" *.txt
grep -E "foo|bar" *.txt

selectively citing the man page of gnu-grep:

   -E, --extended-regexp
          Interpret PATTERN as an extended regular expression (ERE, see below).  (-E is specified by POSIX.)

Matching Control
   -e PATTERN, --regexp=PATTERN
          Use PATTERN as the pattern.  This can be used to specify multiple search patterns, or to protect  a  pattern
          beginning with a hyphen (-).  (-e is specified by POSIX.)

(...)

   grep understands two different versions of regular expression syntax: “basic” and “extended.”  In  GNU grep,  there
   is  no  difference  in  available  functionality  using  either  syntax.   In  other implementations, basic regular
   expressions are less powerful.  The following description applies to extended regular expressions; differences  for
   basic regular expressions are summarized afterwards.

In the beginning I didn't read further, so I didn't recognize the subtle differences:

Basic vs Extended Regular Expressions
   In basic regular expressions the meta-characters ?, +, {, |, (, and ) lose their special meaning; instead  use  the
   backslashed versions \?, \+, \{, \|, \(, and \).

I always used egrep and needlessly parens, because I learned from examples. Now I learned something new. :)

Like TC1 said, -F seems to be usable option:

$> cat text
some text
foo
another text
bar
end of file

$> patterns="foo
bar" 

$> grep -F "${patterns}" text
foo
bar