The ヶ in e.g. 一ヶ月 is a bit of an odd character - it looks a lot like a small version of the katakana ケ, but is it derived from that katakana originally? Or is it a normal kanji? Or is it something else entirely?
It has two main usages:
- As an abbreviation of the counter word 個/箇.
- More often it has a further word after it and it's read か. In this case it's sometimes written as ヵ or even か so the reading is more obvious. Examples: 一ヶ月（いっかげつ） 二ヶ国語 三ヶ所
- Sometimes it's used alone just like 個 is (and it's read こ too), perhaps as shorthand. I've rarely seen people do this, but then again I rarely see handwritten text, where shorthand would be handy. Example: １ヶ（いっこ）
- As something that roughly corresponds to the modern particle の in place names. In this case it's usually read が (especially in old Japanese the particle が has a close resemblance to the modern の). Examples: 西ヶ原（にしがはら） 鳩ヶ谷市
Place names will have some exceptions, as always, but I think these rules cover by far most cases.
It is an abbreviation for the kanji 箇, which is used as a counter word. Although it resembles the katakana character ke (ケ), it is pronounced ka, ga or ko, not ke.