The Dagesh Lene indicates the harder (plosive) form of the double letters:

bet, gimel, dalet, kaf, peh, resh, tav.

In modern Hebrew, only bet, kaf, and peh retain a distinction in pronunciation.

A Dagesh Lene will usually appear when one of the double letters begins a word, or when it begins a new syllable (usually after a closed syllable ending in a silent shewa)

The Dagesh Lene can also appear as the second of a two-consonant cluster of a closed syllable at the end of a word, when both it and the preceding consonant include a silent shewa. (Example: שָׁמַרְתְּ, sha-mar-t)

Vav does not take a dagesh, but a dot inside of it (which looks exactly like a dagesh) marks it as a matre lectionis. See: Shuruq.

Dagesh Forte is used to indicate doubling of a consonant, which also means that it form the ending of a closed syllable with the preceding consonant and vowel, in addition to acting as the beginning a new syllable.

Letters which can take a Dagesh Forte include: zeyin, tet, yod, lamed, mem, nun, samek, tsadi, qof, shin.

A Dagesh Forte can only exist in a medial position; it cannot begin or end a word.

Guttural letters cannot take a Dagesh Forte. They cannot be doubled. The letter resh has some exceptions to this, as it isn't fully treated as a guttural.

Any of the Matres Lectionis (alef, heh, vav, or yod) may have a dot inside of them (which looks identical to a dagesh). This is called a Mappiq, and means that the consonant should be fully pronounced.

For a vav, this is quite rare and may seem confusing as it will appear as what would normally be a shuruq, but the presence of a following vowel will be the clue that it is actually a mappiq.