Hebrew (and Yiddish) uses a different alphabet than English. The picture to the right illustrates the Hebrew alphabet, in Hebrew alphabetical order. Note that Hebrew is written from right to left, rather than left to right as in English, so Alef is the first letter of the Hebrew alphabet and Tav is the last. The Hebrew alphabet is often called the "alef-bet," because of its first two letters.
Note that there are two versions of some letters. Kaf, Mem, Nun, Peh and Tzadeh all are written differently when they appear at the end of a word than when they appear in the beginning or middle of the word. The version used at the end of a word is referred to as Final Kaf, Final Mem, etc. The version of the letter on the left is the final version. In all cases except Final Mem, the final version has a long tail.
Like most early Semitic alphabetic writing systems, the alef-bet has no vowels. People who are fluent in the language do not need vowels to read Hebrew, and most things written in Hebrew in Israel are written without vowels.
However, as Hebrew literacy declined, particularly after the Romans expelled the Jews from Israel, the Rabbis realized the need for aids to pronunciation, so they developed a system of dots and dashes known as nikkudim (points). These dots and dashes are written above or below the letter, in ways that do not alter the spacing of the line. Text containing these markings is referred to as "pointed" text.
Most nikkudim are used to indicate vowels. The table at right illustrates the vowel points, along with their pronunciations. Pronunciations are approximate; I have heard quite a bit of variation in vowel pronunciation.
Vowel points are shown in blue. The letter Alef, shown in red, is used to illustrate the position of the points relative to the consonents. The letters shown in purple are technically consonents and would appear in unpointed texts, but they function as vowels in this context.
There are a few other nikkudim, illustrated and explained below.
The dot that appears in the center of some letters is called a dagesh. With most letters, the dagesh does not significantly affect pronunciation. With the letters Bet, Kaf and Pe, however, the dagesh indicates that the letter should be pronounced with its hard sound (the first sound) rather than the soft sound (the second sound). In Ashkenazic pronunciation (the pronunciation used by many Orthodox Jews and by older Jews), Tav also has a soft sound, and is pronounced as an "s" when it does not have a dagesh.
Vav, usually a consonant pronounced as a "v," is sometimes a vowel pronounced "oo" (u) or "oh" (o). When it is pronounced "oo", pointed texts have a dagesh. When it is pronounced "oh", pointed texts have a dot on top.
Shin is pronounced "sh" when it has a dot over the right branch and "s" when it has a dot over the left branch.
The style of writing illustrated above is the one most commonly seen in Hebrew books. It is referred to as block print or sometimes Assyrian text.
For sacred documents, such as Torah scrolls or the scrolls inside tefillin and mezuzot, there is a special writing style with "crowns" (crows-foot-like marks coming up from the upper points) on many of the letters. This style of writing is known as STA"M (an abbreviation for "Sifrei Torah, Tefillin and Mezuzot," which is where you will see that style of writing.
There is another style used for handwriting, in much the same way that cursive is used for the Roman (English) alphabet. This modern script style is illustrated below, at right.
Another style is used in certain texts to distinguish the body of the text from commentary upon the text. This style is known as Rashi Script, in honor of Rashi, the greatest commentator on the Torah and the Talmud. The alefbet at left is an example of Rashi Script
The process of writing Hebrew words in the Roman (English) alphabet is known as transliteration.
Transliteration is more an art than a science, and opinions on the correct way to transliterate words vary widely. This is why the Jewish festival of lights (in Hebrew, Chet-Nun-Kaf-Heh) is spelled Chanukkah, Hannukah, Hanukkah, and many other interesting ways. Each spelling has a legitimate phonetic and orthographic basis; none is right or wrong.
Each letter in the alefbet has a numerical value. These values can be used to write numbers, as the Romans used some of their letters (I, V, X, L, C, M) to represent numbers. Alef through Yod have the values 1 through 10. Yod through Qof have the values 10 through 100, counting by 10s. Qof through Tav have the values 100 through 400, counting by 100s. Final letters have the same value as their non-final counterparts.
The number 11 would be rendered Yod-Alef, the number 12 would be Yod-Bet, the number 21 would be Kaf-Alef, the word Torah (Tav-Vav-Resh-He) has the numerical value 611, etc. The only significant oddity in this pattern is the number 15, which if rendered as 10+5 would be a name of G-d, so it is normally written Tet-Vav (9+6). The order of the letters is irrelevant to their value; letters are simply added to determine the total numerical value. The number 11 could be written as Yod-Alef, Alef-Yod, Heh-Vav, Dalet-Dalet-Gimmel or many other combinations of letters.
Because of this system of assigning numerical values to letters, every word has a numerical value. There is an entire discipline of Jewish mysticism known as Gematria that is devoted to finding hidden meanings in the numerical values of words. For example, the number 18 is very significant, because it is the numerical value of the word Chai, meaning life. Donations to Jewish charities are routinely made in denominations of 18 for that reason.
Sources: Judaism 101