Which group on the Home tab holds the commands for changing the font of the text?

The first choice (brush) is to keep source formatting.

The arrow button is to merge formatting and the A is to paste the content into the destination document's formatting.

Paste Special... brings up a dialog box that I do not pretend to understand.

Set Default Paste... let's you decide what happens when you simply press Ctrl+V to paste.
It gives far more nuanced control through the Advanced Word Options.

It deletes content from the current location and puts it in the Clipboard.

Another way of looking at this is that it is the beginning of moving text (or graphics) from one part of a document to another
(or to a different document or even program).

The second step - the new location placement is done with the Paste command or button.
 

I strongly urge people to use Styles rather than the Format Painter. In the long run it will make your life much simpler.

Double-clicking on it allows you to paste to different areas using the mouse brush pointer.
 

This launches the Office Clipboard Task Pane which shows items recently added to the Office Clipboard with the latest at the top.

The Office Clipboard can hold 24 items.

If you Copy or Cut from any program while an Office program is open, the content is added to the Office Clipboard as well as to the System Clipboard.

When you paste content, it will be from the System Clipboard (which holds one item).

To use the Office Clipboard, you need to display the Office Clipboard Task Pane.

That pane is anchored to the left side of the Word window by default but can be made to float and can be resized when floating.

Note that if you Copy or Cut material more than once, it will occupy multiple postitions in the Office Clipboard.

Office does not keep track of whether the item is already in the Office Clipboard.

The Clipboard is available in all MS Office programs.

It is cleared if you close all Office programs or if you use the Clear option.

If you use the Clear option, you will also clear the System Clipboard.

These two buttons apply Bold or Italic formatting to text. When the insertion point is inside text that has been
formatted as bold or Italic, these buttons will be shaded.

Bold and Italic are toggle formatting. I.e., if you apply bold to text that is already bold, it is turned off.

Both can be applied to the same text, so that you can have text formatted Bold and Italic.

I tend to use the Strong and Emphasis character styles instead of the direct formatting in case of a theme change.
There is no built-in style for that. Applying the style is not a toggle.
 

Clicking on the Underline button will underscore your text. Clicking the little triangle on the right will give you options for
the type of underline you want. Once you select an option, that option is active during your Word session (including in
different documents). The Underline Color brings up a palette. More Underlines... brings up the Font dialog box which has
access to even more underline types.

You can only apply one type of underlining to a character. This is character formatting so you could apply different types to
different characters in the same word.

If text is already underlined and you click on the Underline button, the underlining will be removed.
 

The Strikethrough button gives you a single line through selected text. A double line is possible through the
Font Formatting dialog box (below).

If this button is clicked on text that already has double-line strikethrough, it changes it to single-line.

If it is clicked on text that already has single-line strikethrough, that is removed.

The Strikethrough button will be shaded if selected text has a single underline applied.
 

These decrease the font size proportionally and lower or raise the baseline.

These buttons are toggles and will be shaded when text is selected to which they apply.
 

Text Effects lets you apply WordArt type appearance to text in the body of your document. Unlike WordArt, Text Effects can be
applied using Styles.

The Text Effects button is available beginning with Word 2010. The screenshot above is from Word 2013; the last three choices
in the menu are not available in Word 2010.

This works as a gallery, changing the appearance of text as you mouse-over a type.

Also, as you mouse-over, if you pause, you will see background information on the effect.

The Text Effects button only works as a drop-down. Unlike the Underline, Highlighting, and Color buttons which also allow choices,
it will not apply an effect upon being clicked. You need to pick something.

Text Effects work best on larger-size text. On body-size text they will make the text unreadable.

For access to all of the options, you need to use the Dialog Launcher.

I do not pretend to understand all of the choices in this. Here is an Office-Watch page on them.
 

If you simply click on the font color button, it will give you the color shown. That color will be the last one applied to text in your Word session.

If you click on the drop-down, it gives you selections and menu choices.

I try to use Theme colors when they work. That is because if a theme is changed, the color is more likely to fit in.

More Colors gives you access to the full palette

Gradient allows setting multiple colors fading - this is much more effective with larger text.
 

As with many of the Groups on the Ribbon, the Font Group has a dialog launcher button in the bottom right corner.

An alternative for reaching this dialog box is the keyboard shortcut Ctrl+D.

This opens a dialog box that gives control over multiple options and gives more options than do the buttons on the Ribbon.

Two not available on the Ribbon buttons are Double strikethrough, and SMALL CAPS. In addition, the Underline style gives
access to many different kinds of underscores.

The Preview box at the bottom previews what you are setting.

Under that are buttons that let you set these settings as the default for new documents (based on this template),
for text effects, and OK/Cancel.

Even more options are available on the Advanced tab of the font dialog box:

These have to do with character rather than line spacing.

Exploration of these options is beyond the scope of this page.

Find (Ctrl+F) opens the navigation pane with the insertion point in a search box

Advanced Find (Ctrl+H, Alt+D) opens the Find dialog box (See Replace below)

Go To... (Ctrl+G) opens a dialog that lets you go to a point in your document
 

Actually, it opens a smaller dialog box with everything above "Search Options" on it. In the smaller version the
button on the left reads "More >>" instead of "<< Less."

Note the Find and Go To tabs at the top. These are the dialog boxes for the Advanced Find and Go To commands.

The Replace dialog can be used instead of the Advanced Find box if you want, just ignore the Replace and Replace All buttons.

Under both the Find what and Replace with boxes are areas for format. These are controlled by the Format and
No Formatting buttons when the cursor is in the box for the text.

There are multiple web pages devoted to this dialog box. Here is a place to start: MVP General Word Help Page