To make a column editable you have to override the isCellEditable method in the TableModel. Creating a TableModel is fairly easy if you inherit AbstractTableModel and I'd recommend it for all but the most simple JTables.
However, adapting the TableModel is only part of what you need to do. To actually get a custom component in the JTable, you need to set a custom cell renderer. To use an interactive custom component, you need to set a custom cell editor. In some cases, it's enough to use slightly modificated versions of the default classes for this.
Editors
If you already have got a custom component is easily done using delegation: Create a new class implementing TableCellEditor, and return a new instance of the component in the getCellEditorComponent method. The paramaters to this method include the current value as well as the cell coordinates, a link back to the table and wether or not the cell is selected.
The TableCellEditor also has a method that is called when the user commits a change to the cell contents (where you can validate user input and adjust the model) or cancels an edit. Be sure to call the stopEditing() method on your editor if you ever programmatically abort editing, otherwise the editor component will remain on screen -- this once took me like 2 hours to debug.
Note that within a JTable editors and only editors receive events! Displaying a button can be done using a renderer. But to get a functioning button, you need to implement an editor with the correct EventListeners registered. Registering a listener on a renderer does nothing.
Renderers
Implementing a renderer is not strictly necessary for what you describe in your question, but you typically end up doing it anyway, if only for minor modifications. Renderers, unlike editors, are speed critical. The getTableCellComponent of a renderer is called once for every cell in the table! The component returned by a renderer is only used to paint the cell, not for interaction, and thus can be "reused" for the next cell. In other words, you should adjust the component (e.g. using setText(...) or setFont(...) if it is a TextComponent) in the renderer, you should not instantiate a new one -- that's an easy way to cripple the performance.
Caveats
Note that for renderers and editors to work, you need to tell the JTable when to use a certain renderer/editor. There are basically two ways to do this. You can set the default cell renderer/editor for a certain type using the respective JTable methods. For this way to work, your TableModel needs to return exactly this type in the getColumnClass(...) method! The default table model will not do this for you, it always returns Object.class. I'm sure that one has stumped a lot of people.
The other way to set the editor/renderer is by explicitly setting it on the column itself, that is, by getting the TableColumn via the getTableColumn(...) method of the JTable. This is a lot more elaborate, however, it's also the only way to have two different renderers/editors for a single class. E.g. your model might have two columns of class String which are rendered in entirely different ways, maybe once using a JLabel/DefaultRenderer and the other using a JButton to access a more elaborate editor.
JTable with its custom renderers and editors is extremely versatile, but it is also a lot to take in, and there are a lot of things to do wrong. Good luck!
How to Use Tables in The Swing Tutorial is mandatory reading for anyone customising JTables. In particular, read and reread Concepts: Editors and Renderers because it typically takes a while for it to "click". The examples on custom renderers and editors are also very worthwhile.