Hello. I am self-taught in Icelandic (still studying) and I have always liked the declension aspect of Icelandic. I'd like to share what I have gathered from it to help other people understand the patterns in it. I would greatly appreciate it if the moderators pinned this thread because I took me a lot of effort to write it and to let it slip to the next pages and be forgotten would be a waste since this is very useful information. Native speakers, do correct me if I wrote something stupid because I'll correct it.
VERBS
Verb conjugation in Icelandic is very unpredictable and random. Verbs are divided in 4 groups: -ar, -ir and -ur verbs (the fourth group being for the ones that don't fall in the previous three ones). All verbs (except for a handful of exceptions) in their infinitive forms end in -a, thus it's impossible to tell just by looking at the verb's infinitive form if it is a -ar, -ir or -ur verb.
A -ar verb (like að tala = to speak) is a verb that when conjugated in the singular third person present tense (he speaks) takes the ending -ar. So að tala > to speak > hann talar > he speaks. There are many verbs that fall in this category. Examples are að nota (to use), að borða (to eat), að kasta (to throw) and að trufla (to bother).
A -ir verb (like að reyna = to try) is a verb that when conjugated in the singular third person present tense (he tries) takes the ending -ir. So að reyna > to try > hann reynir > he tries. There are many verbs that fall in this category. Examples are að senda (to send), að samþykkja (to consent), að heimsækja (to visit) and að heyra (to hear).
-Ar and -ir verbs behave fairly regularly and, once you identify they are -ar/-ir verbs, the conjugation of the present and past tense and the formation of the past participle become pretty predictable.
A -ur verb (like að verða = to become) is a verb that when conjugated in the singular third person present tense (he becomes) takes the ending -ur. So að verða > to become > hann verður > he becomes. There are many verbs that fall in this category. Examples are að selja (to sell), að velja (to choose), að skjóta (to shoot) and að aka (to drive).
-Ur verbs are the most unpredictable ones. They come with vowel shifts and sometimes the past tense bears little to no resemblance to the present tense. Examples:
And, in more extreme cases:
The fourth group is the exception group. Verbs like að vera, að sjá, að bera and að muna (there are others) have all their own conjugation patterns and the only way is to memorize them. Mostly ruleless.
Icelandic verbs also come with a thing called mediopassive voice (miðmynd) which exists in most verbs. It has five uses and is characterized by the ending -st:
Reflexivity—The middle voice form of a verb may be used in lieu of a reflexive pronoun, for example: Þór klæðir sig ⇒ Þór klæðist (‘Þór gets dressed’)
Reciprocity—Here the middle voice is used to mean ‘each other’, for example: Þór talar við Stefán og Stefán talar við Þór ⇒ Þór og Stefán talast við (‘Þór and Stefán talk to each other’)
An alternative meaning—As previously mentioned, some middle voice verbs carry different meanings than their counterparts. Examples include koma (‘to come’) becoming komast (‘to get there’) and gera (‘to do’) becoming gerast (‘to happen’)
The passive—In certain situations, the middle voice may express an idea for which English would use the passive. For example, the phrase, Bíllinn sést ekki, translates as ‘The car cannot be seen’. Most often the middle voice is used in this context when there is no direct reference to any grammatical person.
In reported speech—When the subject of reported speech is the same of that reporting, the middle voice may be used. For example, Hann sagðist ekki lesa bókina, translates to, 'He said (that) he didn't read the book'. Note three special features of this construction: 1) the use of the infinitive 'lesa' in the subordinate clause; 2) the placement of 'ekki'; and 3) the lack of the complementizer 'að', corresponding to English 'that'.
NOUNS
Nouns in Icelandic inflect in four cases (Nominative (nafnfall), Accusative (þolfall), Dative (þágufall) and Genitive (eignarfall)) and can be either masculine, feminine or neuter gendered. There are a few patterns you can learn and keep in mind in order to be able to guess the gender of a noun but don't count on them 100%.
Neuter Nouns: Inflection of neuter nouns in Icelandic is the easiest and most predictable one. The nouns land, hjarta, lyf and klaustur summarize pretty well all the possible stem endings and their patterns.
Feminine Nouns: Inflection of feminine nouns in Icelandic is a bit more diverse but the patterns are mostly predictable. If the noun ends in an -a, it declines like stelpa . If it ends in a consonant, it declines like frétt (though there are feminine nouns whose the plural form -ir becomes -ar like in kinn and vél) and if it ends in -un or -ing it declines regularly and predictably like hugsun and spurning, respectively. Feminine nouns ending in -ur decline like brúður. Some feminine nouns like saga and vika have an additional -n- in the plural genitive forms.
Masculine nouns: These are a nightmare and are often unpredictable. Possible patterns can be (but aren't limited to) hundur, staður, þráður, meðlimur, brandari, botn and others.
A good website to practice the declension is Íslenzka.is so go there practice.