Modern Israeli Hebrew is written without vowel marks (niqqud). Unlike Torah scrolls, which also lack vowel marks, Modern Hebrew does have representations for most of the vowels. How's it done? This page will describe the steps required to turn a Hebrew word with niqqud into an equivalent word in Modern Hebrew.
In this step, any instances of ◌ֹ without ו or ה are turned into וֺ◌. After this stage the word still preserves all of the information about the traditional pronunciation.
Since the difference in vowel length between medium and long length vowels no longer exists in everyday Israeli pronunciation, ◌ִ (short i) can be promoted to י◌ִ (i in liturgical pronunciation) and thus i becomes represented by a full letter י after the niqqud symbols are dropped in the final step. Likewise, ◌ֻ becomes וּ◌ and ◌ָ becomes וֺ◌ (both reduced to a plain ו after the niqqud are removed).
If we simply dropped the niqqud symbols at this point then lots of ambiguity would be created. For example, ו could stand for v, u or o. To reduce the ambiguity a bit, when ו stands for v then it's written twice, as וו in the modern spelling (an idea borrowed from Yiddish). Similarly, in Modern Hebrew, when י stands for y it's written as יי, and when it stands for i or e then those are written using a single י.
The vowel marks are removed, as is the silent sh'vā (lack of vowel) indicator, the dots over שׂ and שׁ and any dageshes (doubling or strengthening), except some dageshes where a כּ, בּ or פּ occurs in an unusual place because a word has been borrowed from English, French, Russian or Yiddish and doesn't fit the standard Hebrew model.
There are some systematic exceptions to the second and third rules. And if one needs to clarify a remaining ambiguity then it's sometimes useful to reinstate the occasional niqqud symbol.