Loŋ S (ſ): The long s is not its own letter, just a different way of writing a lowercase S(compared to s, or the round s). Long s is used everywhere but the last s in a word or in any s adjacent to an f.
Æſh (Æ æ): Ash is a ligature of the letters a and e, representing a vowel sound between those letters.
Eþel (Œ œ): Ethel is a ligature of the letters o and e, representing a vowel sound between those letters.
Inſular g (Ᵹ ᵹ): The insular g represents the /zh/ sound, like the s in measure.
Eð (Ð ð): Eth represents the voiced th sound in words like the.
Yoȝ (Ȝ ȝ): Yogh used to represent the /kh/ sound, which has since disappeared from English. It still takes the place of the letters gh, or z in Scottish words like McKenzie.
Þorn (Þ þ): Thorn represents the voiceless th in words like thing.
Eŋ (Ŋ ŋ): Eng represents the ng sound, taking the place of the letters ng.
Wynn (Ƿ ƿ): Wynn represents the wh sound which exists in some English dialects, and takes the place of wh.
Amperſand (&): Ampersand is a letter representing the word "and", which has not been phased from the Furbish alphabet unlike in other countries. It has seen a comeback recently like Ꝥ.
Ðat (Ꝥ): That is a letter representing the word "that", which after falling out of favor has seen a comeback because of texting and character limits.
Þrouȝ (Ꝧ): Through is a letter representing the word "through", which after falling out of favor has seen a comeback because of texting and character limits.
There are exceptions to these. Thorn would not be in compound words like pothole, for example. Borrowed words, like spaghetti, also do not use these letters, and same with foreign names, unless changed by people to reflect these spellings.
Besides these letters, modern Furbish spellings have been unchanged since English in the late 1600s. Besides British spellings being used in words like colour and defence, other spellings phased out of even England are used, such as connexion, or the long scale for numbers(see table below).