What are the daily, weekly and monthly acts of worship?

Firstly:

The topic of acts of worship and obedience
is very broad, and there is not room to discuss it in full here.

The questioner may refer to the following
books for details on this matter:

·       
At-Targheeb wa’t-Tarheeb
by Imam al-Mundhiri, along with Saheeh at-Targheeb wa’t-Tarheeb and
Da‘eef at-Targheeb wa’t-Tarheeb by Shaykh al-Albaani, for information
on the verdict on the soundness and weakness of the hadiths.

·       
Riyaadh as-Saaliheen
by Imam an-Nawawi, especially the section entitled Kitaab al-Fadaa’il.

Secondly:

The daily acts of worship include the five
daily prayers and doing wudoo’ for them; using the miswaak when doing wudoo’
and praying; praying in congregation (jamaa‘ah); the regular Sunnah prayers,
Duha prayer, qiyaam al-layl (voluntary prayers at night); Witr prayer; the
adhkaar for morning and evening; adhkaar to be recited by day and by night
(when entering and leaving the home, when entering and leaving the mosque,
when entering and leaving the washroom, when eating and drinking, following
the prescribed prayers, and so on); repeating after the mu’adhdhin.

The weekly acts of worship include Jumu‘ah
prayer; reading Soorat al-Kahf on the night before Friday and on Friday;
sending a lot of blessings upon the Prophet (blessings and peace of Allah be
upon him) on the night before Friday and on Friday; fasting on Mondays and
Thursdays.

Monthly acts of worship include fasting
three days of every month (and it is preferable for that to be on al-ayaam
al-beed, i.e., the 13^th, 14^th and 15^th
of the Hijri month).

Annual or occasional acts of worship
include: fasting Ramadan; praying Taraweeh in congregation in the mosque;
offering the Eid prayers; Hajj for those who are able to do so; giving
zakaah for those for whom the conditions of it being obligatory are
fulfilled; spending the last ten days of Ramadan in i‘tikaaf; fasting six
days of Shawwaal; fasting ‘Ashoora’ and a day before it or after it; fasting
the day of ‘Arafah; doing a lot of good deeds in the first ten days of
Dhu’l-Hijjah.

There are also deeds that are not
connected to a particular time, so they are prescribed at all times,
including deeds of the heart as well as physical actions. These include:
offering voluntary prayers at times other than the times when praying is
disallowed; observing voluntary fasts; ‘umrah; remembering Allah (dhikr);
reading Qur’an; sending blessings upon the Prophet (blessings and peace of
Allah be upon him); supplication (du‘aa’); praying for forgiveness (istighfaar);
honouring one’s parents; upholding ties of kinship; giving charity;
spreading the greeting of salaam (peace) among the Muslims; having a good
attitude; controlling one’s tongue; loving Allah, fearing Him and putting
one’s hopes in Him; putting one’s trust in Him; contentment; certainty of
faith; seeking His help, may He be glorified and exalted.

And there are good deeds that are done for
a reason, in which case it is prescribed to do them when that reason is
present. These include: visiting the sick; attending funerals; offering the
funeral prayer; offering condolences; saying Yarhamuk Allah (may
Allah bless you) to one who sneezes; returning greetings of salaam;
accepting invitations; praying istikhaarah; offering the prayer of
repentance (salaat at-tawbah); the eclipse prayer; prayers for rain;
reconciling between disputing parties; lowering the gaze; refraining from
harming others; bearing annoyance and calamity with patience; and so on. 

The salaf (early generations) liked to
combine four acts of worship on one day, namely: fasting, feeding the poor
(charity), attending funerals and visiting the sick. The Prophet (blessings
and peace of Allah be upon him) said concerning these actions: “These
qualities are not combined in a man but he will enter Paradise.”Narrated by
Muslim (1028). 

And Allah knows best.