To express period and frequency—in other words, to say how many times something happened per day, week, and year, and so on—we need a counter with the target particle (see here for an introduction to counters in Japanese).
[Period] + に + [Number] + [Counter]
This structure is most often used with the counter 回, which means “times” (e.g. I go back to my hometown 3 times per year”).
週に５回。
Five times per week.
年に２回、実家に帰る。
To return to your hometown twice per year.
Because counters act as “floating adverbs” in Japanese, word order is flexible. The frequency counter can be placed immediately after the object particle, or before the object entirely.
週に本を３冊読みます。
To read 3 books per week.
週に３冊、本を読みます。
To read 3 books per week.
In fact, the target particle に attached to the period is often omitted in everyday conversation.
週４回ジムに通う。
To go to the gym four times per week.
年２回海外に行きます。
To go abroad twice per year.
The “1” Rule for Periods
While saying 週に (per week) and 年に (per year) is perfectly natural, saying 日に or 月に is incorrect. To express “per day” or “per month,” you must attach the number 1 to the beginning. Pay close attention to the pronunciation exceptions.
１日に
Per day (Note: always read as “ichinichi”, never “tsuitachi”).
１ヶ月に
Per month.
This “1” formula is mathematically consistent and can also be applied to weeks and years to create universally safe defaults.
１週間に
Per week.
１年に
Per year.
Note that １年間に is also grammatically correct. Whether or not “間” (a character that denotes duration) is required depends on whether we are talking about a point in time or a duration. This is most obvious when we’re talking about hours.
１時。
1 o’clock (a point in time).
１時間。
One hour.
Weeks are treated as a point in time, as well, because １週 can mean the first week of an month (or an event), hence why to make it a duration of one week we must add 間.
Conversely, １年 inherently means a period of one year, and so the 間 is optional. １日 (one day) does not take 間 for the same reason.
Months are a bit weird. １ヶ月 is a block counter itself and inherently mean duration, and so 間 is never appended.
The ヶ is actually a visual abbreviation of the kanji 箇. In traditional Japanese, 箇 is a general counter for items or places. Hundreds of years ago, when people wrote 箇 quickly with a brush, they often abbreviated it to the top radical (the bamboo radical: 竹). Over time, that shorthand evolved into the symbol ヶ.
Asking “How Often?”
To ask someone about their frequency, use the question word 何回 (how many times) or the phrase どのぐらい (how often).