Select the text in visual mode (I assume that's what you're doing), then press : to start typing a command, you'll see something like this appear in the command line:
:'<,'>
That means that the command will apply to the selection. Then type s/search/replace/ and hit enter. (Add a g after the third slash if you want to replace all matches, and a c if you want a confirmation for every replace)
Most of the other solutions suggested here work over the ENTIRE line in which the selection occurs, which may not be what you want.
To search and replace ONLY in the selection, first visually select the text, then use a command like so:
:%s/\%VSEARCH/REPLACE/g
This will do the search and replace only in the visually selected section, replacing SEARCH with REPLACE. If you have more than one line selected, this will work over multiple lines too.
The range of Ex commands are specified line-wise (see *cmdline-ranges*), and when : is pressed while there is a visual selection, the line range is automatically specified on the command line as '<,'> (see *v_:*), which makes the :s[ubstitute] command operate on the whole lines unless the visual selection boundaries are specified in the search pattern with \%V (see */\%V*), e.g. /\%Vvi\%Vm matches "vim" only within the visual selection, where the end of the selection is specified right before the end of the search pattern since each \%V specifies the next character as the start or end of the visual selection, and thus /\%Vvim\%V would require the visual selection to continue after 'm' to match "vim". Note that using the second \%V in a search pattern isn't necessary unless a match is required to be right at the border of or only partly in the visual selection.