In general the basic principal for cleansing the najasah until there is no smell, no colour and no taste/ feel. And the best way to clean najasah is using water.
Narrated Abu Sa’id Al Khudri, Allah’s Messenger sallallahu alaihi wasalam said, “Water is tahoor (purifying)
In fiqh all things are considered pure unless there is evidence otherwise.
1. Human urine and faeces
They are impure
Abu Sa’eed al-Khudri has said:
“The Messenger of Allaah (sallallaahu `alaihi wa sallam) prayed with us one day. Whilst he was engaged in the prayer he took off his shoes and placed them on his left. When the people saw this, they took off their shoes. When he finished his prayer he said, Why did you take your shoes off? They said, `We saw you taking your shoes off, so we took our shoes off.’ He said, Verily Jibreel came to me and informed me that there was dirt – or he said: something harmful – (in another narration: filth) on my shoes, so I took them off. Therefore, when one of you goes to the mosque, he should look at his shoes: if he sees in them dirt – or he said: something harmful – (in another narration: filth) he should wipe them and pray in them.
(by the way Prophet Muhammad sallallahu alaihi wasalam used to pray with his shoes on in the masjid. At that time masjid has no carpet like how we have nowadays. And the floor is probably soil.
Bukhari :: Book 1 :: Volume 4 :: Hadith 221
Narrated Anas bin Malik:
A Bedouin came and passed urine in one corner of the mosque. The people shouted at him but the Prophet stopped them till he finished urinating. The Prophet ordered them to spill a bucket of water over that place and they did so.
The fact that in both hadith the filth is told to be washed, this indicates that these are impure.
2. Al Madhi and Al Wadi
Excrement that comes out from your peeing area. Sometimes (more for the teenagers and adults) we have some liquid coming from or private parts. It is not like your pee. It is thick and white and sticky. This is najis. You must wash like you wash when you pee and retake your wudhu’.
Bukhari :: Book 1 :: Volume 5 :: Hadith 269
I used to get emotional urethral discharge frequently. Being the son-in-law of the Prophet I requested a man to ask him about it. So the man asked the Prophet about it. The Prophet replied, “Perform ablution after washing your organ (penis).”
Purification (Kitab Al-Taharah)
Dawud :: Book 1 : Hadith 210
Narrated Sahl ibn Hunayf:
I felt greatly distressed by the frequent flowing of prostatic fluid. For this reason I used to take a bath very often. I asked the apostle of Allah (peace_be_upon_him) about this. He replied: Ablution will be sufficient for you because of this. I asked: Apostle of Allah, what should I do if it smears my clothes. He replied: It is sufficient if you take a handful of water and sprinkle it on your clothe when you find it has smeared it.
3. Excrement of animals
Bukhari :: Book 1 :: Volume 4 :: Hadith 158
The Prophet went out to answer the call of nature and asked me to bring three stones. I found two stones and searched for the third but could not find it. So took a dried piece of dung and brought it to him. He took the two stones and threw away the dung and said, “This is a filthy thing.”
So excrement of animals is najis
4. Menstrual Blood
Bukhari :: Book 1 :: Volume 6 :: Hadith 304
Narrated Asma’ bint Abi Bakr:
A woman asked Allah’s Apostle, “O Allah’s Apostle! What should we do, if the blood of menses falls on our clothes?” Allah’s Apostle replied, “If the blood of menses falls on the garment of anyone of you, she must take hold of the blood spot, rub it, and wash it with water and then pray in (with it).”
Narrated by Abu Hurayrah that Khawlah bint Yasaar said, “O Messenger of Allah! I have only one garment and when I have my menstrual period I get blood on it, so what should I do? He sallallahu alaihi wasalam replied: “Once you have cleansed yourself from your period, wash the place where the blood was and then pray in it.” She said, ‘Even if the traces of it are not removed, O messenger of Allah. He sallallahu alaihi wasalam said, “The water is sufficient for you and the traces will not harm you.”
Menstrual blood is impure. Thus try to wash as much as you can but sometimes blood can be a bit stubborn. Thus the Prophet sallallahu alaihi wasalam said, the traces of blood will not harm you.
4. Dog saliva
The Book of Purification (Kitab Al-Taharah)
Muslim :: Book 2 : Hadith 549
Abu Huraira reported: The Messenger of Allah (may peace be upon him) said: The purification of the utensil belonging to any one of you, after it is licked by a dog, lies in washing it seven times, using sand for the first time.
If a dog licks your utensil, you need to wash it seven times and the first one to use dust. This utensil is the one that you would use for ablution.
5. Dead animals.
Dead animals that die a natural death without being slaughtered are not halal to eat according to syariah. But there are exceptions
i. Dead fish and locusts
Ibn Umar radiallahhu anhu said, “Prophet sallallahu alaihi wasalam said,
“Two dead things and two kinds of blood have been permitted to us: As for two dead things, they are fish and locusts. And as for two kind of blood, they are liver and spleen. (Bahyaqi)
ii. Dead things which have no flowing blood like ants, bees and such
Beginning of Creation
Bukhari :: Book 4 :: Volume 54 :: Hadith 537
Narrated Abu Huraira:
The Prophet said “If a house fly falls in the drink of anyone of you, he should dip it (in the drink), for one of its wings has a disease and the other has the cure for the disease.”
This indicates that fly is not najis.
iii. The bones, horns, claws, hair and feathers of dead things
hadeeth of Al-Bukhaari, narrated in a mu’allaq  form proves it; he said: “Az-Zuhri said, concerning the bones of dead creatures, such as elephants and the like: “I have seen some people from among the scholars of the Salaf combing their hair with (combs made from) them and writing upon them and they see no objection to it.” And Hammad said: “There is nothing wrong with using the feathers of a dead (bird).”
6. Donkey’s flesh
Bukhari :: Book 7 :: Volume 67 :: Hadith 436
Narrated Anas bin Malik:
Someone came to Allah’s Apostle and said, “The donkeys have been (slaughtered and) eaten. Another man came and said, “The donkeys have been destroyed.” On that the Prophet ordered a caller to announce to the people: Allah and His Apostle forbid you to eat the meat of donkeys, for it is impure.’ Thus the pots were turned upside down while the (donkeys’) meat was boiling in them.
Wild donkeys are permissible though. This ruling is meant for domesticated donkeys.
7. Cleansing the hem of a woman’s dress
Purification (Kitab Al-Taharah)
Dawud :: Book 1 : Hadith 383
Narrated Umm Salamah, Ummul Mu’minin:
The slave-mother of Ibrahim ibn AbdurRahman ibn Awf asked Umm Salamah, the wife of the Prophet (peace_be_upon_him): I am a woman having a long border of clothes and I walk in filthy place; (then what should I do?). Umm Salamah replied: The Apostle of Allah ( peace be upon him) said: What comes after it cleanses it.
So do not worry too much on the dust and slight dirt on your abaya until of course some foul smell of clear najis can be seen on it.
8. Urine of breastfed baby
Narrated Abu As Samh, Allah’s Messenger sallallahu alaihi wasalam said,
“The urine of a baby girl should be washed off and the urine of a baby boy should be sprinkled.”
This only apply to babies who are exclusively breast fed.
It does not mean the baby boy’s urine is not najis.
It is just the shariah made the cleaning easier.
Fiqh Course Volume 1 : Taharah, Salaah & Janaa’iz. IIPH