Writing is prohibited on Ḥol Ha-mo’ed, just as other melakhot are. Therefore, one may not write even just a single letter of a Torah scroll, a mezuza, or tefilin. It is also prohibited to draft legal documents, do paperwork for business, take a test, or write a paper or book report (SA 541:1 and 6). Even for festival needs, skilled writing is prohibited. This means writing (whether in cursive or print) while making special efforts to write aesthetically or precisely. However, for festival needs it is permitted to write normally, without making efforts. Therefore, one who needs to buy food on Ḥol Ha-mo’ed may write a shopping list.
One may also write a letter to a friend with normal handwriting. Doing so is a festival need, as it gives people enjoyment and strengthens friendships. This is on condition that he does not plan to write the letter on Ḥol Ha-mo’ed. If one wishes to write to his friends, he should not delay it until Ḥol Ha-mo’ed (MB 545:31).
Similarly, one who wishes to give a present to his friend may write out a card, and if it is a book he may inscribe it (SA 545:5). Whenever writing is permissible on Ḥol Ha-mo’ed, some are stringent to write the first line crookedly. However, one who wishes to be lenient may be, as this is the position of most poskim in practice. (See MB ad loc. 35.)
“Writing” with a computer is considered unskilled. Thus one may type a shopping list on a computer or smartphone, and send an email or text message, but only on condition that it is serving a festival need, as even unskilled labor is forbidden if it does not fulfill a festival need.
If one is studying Torah and finds that taking notes (whether handwritten or typed) helps him focus, he may do so. This writing is for the sake of a mitzva and is thus permissible. (In 12:11 and 12:13 below, we will explain about writing for the sake of a mitzva.)
Printing with a computer printer is considered skilled labor by some of the poskim. Even though sending something to print is very simple, the quality of the result is professional. Ideally, it is proper to defer to the stringent opinion and avoid printing on Ḥol Ha-mo’ed. (In 12:14 below, we will explain about writing for a court case and to prevent a loss.)
“Writing” on a computer without printing: Some say that there is no problem with this, and that it is permissible even for non-festival needs, since what one is doing is virtual, not real. Letters are being formed only electronically, which is similar to non-permanent writing. Doing it to make a living is still prohibited (Ḥol Ha-mo’ed Ke-hilkhato 6:98). Others maintain that “writing” on the computer is considered unskilled labor, and may be done only for a festival need. In contrast, what isn’t saved on the computer, such as “writing” in a game, is entirely permissible. This is the halakha (R. Eliyahu, Ma’amar Mordechai 19:54; Ḥut Shani 19:6).
Computer printing: Some say that this is skilled labor, because the resulting printout is deemed professional (based on Eliya Rabba 460:6). Others maintain it is unskilled, as everyone knows how to do it (based on Eshel Avraham [Buczacz], second edition, §545). See Ḥol Ha-mo’ed Ke–hilkhato 6: 89 and Piskei Teshuvot 545:2. In practice, it would seem that le-khatḥila one should be stringent and avoid printing even for festival use. However, when necessary, such as for a Torah class, one may rely on the lenient position, since the rationale makes sense. If the avoidance of printing something out will lead to less Torah being learned, the printing is permitted to prevent the loss. One may also be lenient in other times of necessity, because according to most poskim this is a case of doubt about a rabbinic law. For even those who maintain that melakha on Ḥol Ha-mo’ed is prohibited by the Torah, it is reasonable to assume that this is limited to major melakha, or that which is involved in making a living.