Siman 531
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א מִצְוָה לְגַלֵּחַ בְּעֶרֶב יוֹם טוֹב.
1 The Laws of Shaving on Chol Hamoed, 8 Seifim: It is a mitzvah to shave on the day before a holiday.
ב אֵין מְגַלְּחִין בַּמּוֹעֵד, אֲפִלּוּ אִם לֹא גִּלַּח קֹדֶם מוֹעֵד.
2 One may not shave during the holiday, even if he shaved before the holiday.
ג אֲפִלּוּ אִם הָיָה אָנוּס וּמִפְּנֵי כָּךְ לֹא גִּלֵּחַ בְּעֶרֶב יוֹם טוֹב, אֵינוֹ מְגַלֵּחַ בַּמּוֹעֵד; וְהוּא הַדִּין לְמִי שֶׁהָיָה חוֹלֶה וְנִתְרַפֵּא בַּמּוֹעֵד.
3 Even if one was forced and thus did not shave on the day before the holiday, he should not shave during hol hamoed. This is also the rule for one who was sick and got better during the holiday.
ד וְאֵלּוּ מְגַלְּחִין בַּמּוֹעֵד; מִי שֶׁיָּצָא מִבֵּית הַשִּׁבְיָה וְלֹא הָיָה לוֹ פְּנַאי לְגַלֵּחַ קֹדֶם הַמּוֹעֵד, וּמִי שֶׁיָּצָא מִבֵּית הָאֲסוּרִים וַאֲפִלּוּ הָיָה חָבוּשׁ בְּיַד יִשְׂרָאֵל שֶׁהָיוּ מַנִּיחִין לוֹ לְגַלֵּחַ, וְכֵן הַמְּנֻדֶּה שֶׁהִתִּירוּ לוֹ בָּרֶגֶל, וְכֵן מִי שֶׁנָּדַר שֶׁלֹּא לְגַלֵּחַ וְנִשְׁאַל עַל נִדְרוֹ בָּרֶגֶל, וְכֵן הַבָּא מִמְּדִינַת הַיָּם בְּחֹל הַמּוֹעֵד, אוֹ שֶׁבָּא בְּעֶרֶב הָרֶגֶל וְלֹא הָיָה שְׁהוּת בַּיּוֹם לְגַלֵּחַ, וְהוּא שֶׁלֹּא יָצָא מֵאֶרֶץ יִשְׂרָאֵל לְחוּצָה לָאָרֶץ לְטַיֵּל.
4 The following people may shave during the holiday: he who left captivity and did not have an opportunity to shave before the holiday; he who left jail, even if he was imprisoned by Jews who would have allowed him to shave; he who was banned [formally by the community] and allowed [back into the community] during the holiday; he who vowed not to shave and asked for the nullification of his vow during the holiday; he who arrived from abroad during hol hamoed or who arrived on the day before the holiday but didn't have time that day to shave, assuming that he did not go from Israel to outside of Israel for recreational purposes.
ה אַף עַל פִּי שֶׁהִתִּירוּ לְהִסְתַּפֵּר, לֹא יִסְתַּפֵּר בִּרְשׁוּת הָרַבִּים אֶלָּא בְּצִנְעָה.
5 Even in instances where it is permitted to get a haircut, one should not get a haircut in the public domain. Rather, one should do this in private.
ו קָטָן מֻתָּר לְגַלֵּחַ בַּמּוֹעֵד, אֲפִלּוּ נוֹלַד קֹדֶם הָרֶגֶל; וַאֲפִלּוּ בְּפַרְהֶסְיָא שָׁרֵי (וְכֵן מַשְׁמָע מִמָּרְדְּכַי).
6 A child can be shaved during the holiday, even if he was born before the holiday (and this is even allowed in public) (this follows from the Mordechai).
ז אָבֵל שֶׁחָל שְׁבִיעִי שֶׁלּוֹ בְּשַׁבָּת עֶרֶב הָרֶגֶל, מֻתָּר לְגַלֵּחַ בְּחֹל הַמּוֹעֵד. הַגָּה: מִי שֶׁהֵמִיר דָּתוֹ וְחָזַר בִּתְשׁוּבָה, וְדַרְכּוֹ לְגַלֵּחַ, מֻתָּר לְגַלֵּחַ בַּמּוֹעֵד (תְּרוּמַת הַדֶּשֶׁן סי' פ"ו).
7 If a mourner's seventh day [of mourning] falls on a Shabbat that is the day before a holiday, he is permitted to shave on hol hamoed. Rema: He who left Judaism, returned, and normally shaves is permitted to shave on hol hamoed (Trumat Hadeshen chapter 86).
ח כָּל אָדָם מֻתָּר לִטֹּל שָׂפָה בְּחֹל הַמּוֹעֵד. הַגָּה: אֲפִלּוּ בְּפַרְהֶסְיָא; וּמֻתָּר לַחוֹף וְלִסְרֹק רֹאשׁ בַּמּוֹעֵד, אַף עַל פִּי שֶׁמֵּשִׁיר שֵׂעָר, וְאֵין בָּזֶה מִשּׁוּם גִּלּוּחַ (מָרְדְּכַי רֵישׁ מ"ק).
8 Every man is permitted to remove his mustache on hol hamoed. Rema: Even in public. It is permitted to rub the head and to comb even though this will remove hair - it is not considered shaving (Mordechai at the beginning of Moed Katan).