Rooh: My question is that what exactly happens to soul after death. Where it goes and in how many days it takes birth again?
Swami Ram Swarup: In this regard, I paste my articles below:-

SOUL NEVER DIES

In this connection, Rigved mantra 10/124/2 states that soul fearing death desires to seek a secret place where he could save himself from death. When he seeks shelter of Almighty God, then leaving behind the fear of death, he gets salvation. In Rigveda mantra 10/124/4 soul states that I have occupied this body since a number of years, now I leave my body to attain Almighty God. The idea of the said two mantras is that it is a nature of soul to fear death, based on the experiences of numerous previous births. Secondly, the living body is to be left one day. This process is eternal. Now see Rigved mantra 10/136/6 wherein it is stated that soul is eternal i.e., soul neither takes birth nor meets with death. It is only human body which is made of five non-alive elements i.e., earth, water, space, air and fire. So, human-body gets destroyed and not the soul, who resides within body and therefore soul has no parents because it never takes birth.

Next mantra 7 states the human body is meant to meet with death. When we see the respiratory system in any body then only do we state that the person is alive. Based on the eternal, fundamental knowledge, Yog shastra sutra 4/33 states that all the matters made of Prakriti are competitors of Kshann (the smallest fraction of time).I mean to say, just after the passing away of one Kshann, the next Kshann comes and the matter being the competitor of Kshann attains his next stage i.e., it gets changed. The matter changes itself while competing with Kshann. Kshann gets changed and so does the matter and the matter attains its next stage.

For example- A pot made of clay gets changed day by day and one day it gets destroyed automatically. It is not necessary that pot needs to be destroyed by any person. But being the nature of Prakriti, from which clay and then pot is made, the pot is liable to get destroyed one day automatically. So is the case of human body made of Prakriti. Human body is changing itself day by day and one day it shall be destroyed automatically but soul residing in it is unchangeable and immortal. So the death of human as well as every living body is guaranteed to meet with the death. In this connection, you may also refer Bhagwad Geeta shloka 2/23 wherein Sri Krishna Maharaj states that human body gets destroyed and not the soul.

After death

Yajurved mantra 3/55, says, “DEVAIYAH JANAH NAH PUNAH MANAH DADATU” i.e., by blessings (preach and true education of Vedas) may learned Acharya give us next birth of human being so that we may again be able to learn the truth of Vedas and to get salvation. So one must always adopt true path by which he gets rebirth of human being to continue the real spiritualism to get salvation etc., because Atharvaved mantra 9/10/16 further says that human being who has done pious deeds and adopted true path they get pious human body in the next birth, otherwise soul gets the lowest/contemptible body, like animals, birds etc. Mantra is APAANG PRAANGETI SWDHAYAA GRIBHITAH AMARTYO MARTYENAA SAYONIHI. TA SHASHVANTA VISHUCHINA VIYANTA NYA NYAM CHIKYURN NI CHIKYURNYAM.

Soul according to its good or bad deeds(APANGETI) takes bodies of animals, birds, insects etc., and (PRANG) bodies of Rishis, Munis, i.e., (uuch Yoni) best bodies after leaving the present body. The soul (SWDHAYAA GRIBHITAH) duly attached with its own power of taking birth according to pious deeds and sins, enters other bodies (AMARTAYAH) though the soul is away from death, being immortal but after death of bodies, takes new bodies. These ideas of Vedas has very well been mentioned in Bhagwad Geeta shlok 2/20 wherein Yogeshwar Shri Krishna says (AJO NITYAH SHASHWATOAYAM PURAANNO NA HANYTE HANYAMANNE SHARIRE ) i.e., the soul is (AJAH NITAYAH SHASHWATOH) never takes birth and is eternal (NAHANYATE HANAYMANNE SHARIRE) in fact after death of body too soul is never dead being immortal. (TASHASHVANTA) this process of death and birth of bodies and souls is eternal.

(VISHUCHINA VYANTA) soul and bodies go far away to different directions [soul goes to Savita etc., {given below} according to Yajurved chapter 39 and then takes birth and gets another body and five elements of body go to space and are mixed within air, fire etc., according to Yajurved mantra 40/15] (ANYAM NICHIKYHU) many learned know about this fact (ANYAM NICHIKYHU) another who lack knowledge of Vedas, do not know the fact, i.e., we mostly know our body but not ourselves, i.e., soul. Death is sure i.e., the body will have to be cremated one day.
In Atharvaved mantra 8/8/11 ‘Yamdut’ means = ‘YAM’ means God, and ‘dut’ means storm, cyclone, flood, earthquake, heavy rains, etc., etc., in mantra the air is Yam. So when a soul is to leave the body then by the power of God, sutratma air enters the body and takes the soul out of it then goes to Savita, etc.

In 39th chapter of Yajurved the process of this cremation is mentioned. This process is also called as “NARMEDH YAJYEN”, “PURUSH MEDH YAJYEN” and “DAH KARAM” and “ANTEYESHATI KARAM”. Atharvaved mantra 10/8/26 says “YEH CHAKAR SAH JAJAR” means He (God) who makes the body, He destroys the same one day. Sense of Yajurved mantra 39/5 is that when the soul leaves the body then the soul wanders in so many places, takes another body according to its previous deeds (karmas). Yajurved mantra 39/6 says that the soul after leaving the body, on the first day goes to Savita (sun), second day agnihi (fire), third Vaayu (normal air), fourth Aditya, fifth chandrma (moon), sixth ritu (seasons), seventh marutah, eighth brihaspati (tiniest air), ninth mitrah (breathing), tenth varunah (udan air), eleventh indrah (electricity), twelfth Vishvedevah (in all divine qualities). Then, after wandering in sky, gets body according to previous deeds. So these twelve days are completed, then after 13 days the soul takes another body. Rigved mandal 10 sukta 135 says that normally soul after getting body faces the result of its past lives’ deeds and under influence of illusion (duly attracted towards illusion) does sins and again gets birth to face the sins. The soul is immortal and always separate from body. When an aspirant meets with a learned Acharya and gets spiritual education, then the fourth mantra says that the soul gets salvation.