On Chol Hamoed (the intermediate days of Sukkot and Pesach), some work is prohibited, similar to a holiday, while some is permitted, similar to a weekday. These rules are discussed extensively in Shulchan Aruch Orach Chayim 530-548. What follows is a breif summary of the most relevant and practical rules mentioned there.
There are three main goals for which work may be done on Chol Hamoed. First, if it is for enjoyment on the holiday, such as driving to a recreational activity. Second, if neglecting to do it may result in a financial loss, such as endorsing and depositing a check. Third, if postponing it until after the holiday will result in the opportunity being lost, such as buying an item that is on sale (other shopping for items that will not be used on the holiday should be avoided). Work not falling into one of these categories is generally prohibited on Chol Hamoed.
What type of writing is permitted on Chol Hamoed? One should certainly not do professional level calligraphy or artwork, unless it is needed for the holiday. Any information that may be forgotten is considered like an opportunity that can be lost, and thus one is permitted to take notes on a lecture, to write down a phone number, or to record financial transactions. It is customary to do these in an unusual manner, such as writing perpendicular to the direction of the lines on lined paper. One may also write letters to friends, as this is an enjoyable activity that is part of celebrating the holiday. Typing on a computer screen is permitted for any goal, and may be preferable to writing on paper, but some prohibit printing with a computer printer, if not for one of the permitted goals listed above. Any time that failing to write will prevent another activity that is part of celebrating the holiday, one is permitted to write. Thus, if one needs to sign something in order to enter an attraction, he is permitted to do so, as attending the attraction is part of his celebration of the holiday.
Laundry and shaving were categorically prohibited on Chol Hamoed, in order to ensure that people will be motivated to make these preparations in advance of the holiday. One may not launder or shave on Chol Hamoed even if this is needed to enhance the holiday. Still, there are several important exceptions. Towels and the like that are constantly being soiled are permitted to be washed, as are the clothes of small children which need frequent laundering. If one needs clothing for the holiday and did not launder it in advance, it may be preferable to buy new clothing rather than to launder one's current clothing; a rabbi should be consulted in this situation.
Rabbi Soloveitchik maintained that today, shaving has become a daily routine, and that allowing it on chol hamoed will not have the effect of causing people to skip it on Erev Yom Tov. Based on this assumption, daily shaving would be permitted and even encouraged as a means of honoring Chol Hamoed. Different communities have different practices in this regard, and all are valid according to halacha.
The goal of prohibiting work on Chol Hamoed is to foster a festive atmosphere and to help us have a sense of holiday on these days. For the same reason, it is appropriate to mark Chol Hamoed with festive meals and gatherings, to sing, to study the mitzvot of the holiday, and to wear festive clothing. It is always good to have a halachically mandated reason for fun and celebration, and we should maximize the holiday aspect of Chol Hamoed to the best of our ability.