How do I wrap text in MS Project? Is the process the same as in other MS programs?

You can increase the height of rows in any sheet view, and wrap text in them to display all text when it's too long to be fully visible in a field, without having to increase the field width.

To increase the height of a row in your project, click in the leftmost column (the Task ID field) to select the row.
To increase the height of multiple rows, hold down CTRL, and then select the rows you want.

Drag the bottom margin of the row heading (the leftmost cell of the row).
Text will automatically wrap as you increase the height of the row.
Notes

To increase the height of all rows in your project, click the Select All button, and then drag the bottom margin of any row heading.

In order for text to wrap in a row cell, the text needs to have at least one space within it so that Project knows where to automatically break a line for word wrapping. You cannot manually control where the line break will occur.

Text wrapping will only occur if the text is too long for the width of the row cell. If the text fits on one line, you cannot manually create a line break. In this situation you can only create a line break by narrowing the column.

A list of names in the Resource Names column of the Gantt Chart and other sheet-like views will not wrap unless there is a space in an individual's name, such as between a first name and last name. If your resources are identified by only first names, then the list of names in the Resource Names column will not wrap.