There are three terms - Jap or Jaap, Anushthaan and Purashcharan. One must clearly understand the difference among the three -

Anushthaan is the biggest word, and it includes many Kriyaa (processes) - from Mantra Sanskaar to Utkeelan, and Purashcharan is only a part of it.

Purashcharan is the main chanting period, but it also includes 5 parts. If one cannot do all the parts as prescribed, one can do Jaap as described below --
(i) Jap - 125,000 times
(ii) Havan - (if one cannot do Havan, then do 1/10th number of the Jap = which will be 12,500 Jap)
(iii) Tarpan - (if one cannot do Tarpan, then do 1/10th of the number of the Havan = which will be 1,250 times Jap)
(iv) Maarjan - (if one cannot do Maarjan then do 1/10th of the number of the Tarpan = which will be 125 times Jap)
(v) Braahman Bhojan - (if one cannot do Braahman Bhoj, then do 1/10th of the number of the Maaarjan = which will be 12 times Jap)

Thus Jaap is just a part of Purashcharan. Although Jap also have sub parts, which will be your Dainik Poojaa Vidhaan (rules) for that particular Saadhanaa of that particular Devtaa (including his all Kavach, Viniyog, Nyaas, Yantra, Aavaran Poojaa, etc.... ). In reality, the main time limit is set for Jap. So if it is written that Mantra Siddhi is done by 1.25 Lakh Jap... and lets say time limit is 11 Days... then one has to chant 101 Maalaa per day for 11 Days. If the time limit is for 21 days, then 61 Maalaa per day for 21 days. And if the time limit is in 40 days, then 33 Maalaa per day... and so on.

These are the set Vidhaan. After one has finished the Jap, one has to do Havan.
If one cannot do actual Havan, he should do twice the Jap. In this 125,000 example, one has to chant the same Mantra in the same ritualistic technique twice (250,000 times). But one has to mention this in the beginning of the Sankalp of Anushthaan only that he will be doing twice the Jap in lieu of Havan... or after the Jap one has to take another Sankalp for twice Jap in lieu of Havan. So it means that one has to chant 25,000 Mantra more in lieu of Havan, so it will be 21 days were for Jap - 61 Mala per day for 5 days for Jap in lieu of Havan. (6100 * 5 = 30,000, yes this is the figure, more than 25,000... or if one is lazy, then 61 Maalaa per day for 3 days and 71 Maalaa for the 4th day, but ideal is 61 Malaa per day for 5 days)

After that Tarpan - 1250 times
then Maarjan  - 125 times
then Braahman Bhojan - 12 times

If one can do actual Kriyaa of these steps, very good, or else use twice the Jap in lieu of this method...
The Tarpan, Maarjan and Braahman Bhojan are done on the last day of the whole Anushthaan, and its best to be able to meet Gurudev on last day if possible.

Method of a Normal Purashcharan
A normal Purascharan means 1.25 Lakh Jap of any Mantra within 5 or 11 or 21 or 40 days depending upon the capacity of the Saadhak. Basically a few rules are to be followed during the Purashcharan -

1. day and time of starting Jap - like Amrit or Mahendra Kaal.
2. color of Dhotee or Saaree.
3. direction of sitting
4. food - Saattwik food with out onion and garlic.
5. remaining silent
6. positive thinking
7. importantly faith in one's Guru and his Mantra
8. two times bath is best
9. can have fruits
10. eating once a day is best but if its hard two times is better, one time with fruits like if doing Bagalaamukhee Mantra Jap daily mango is best if Mahaakaalee Mantra Jap then any red fruit is best.
11. to cut down the Dosh of farting, burping or feeling sleepy during Jap always have a copper tumbler with water ready if you fart dip your left hand fingers thumb and Jupiter finer and touch your both ears.
12. rest in Guru Dev's hands because he is the tree and we are the small branches; if we cut ourselves from Guru Dev we will dry up and we becomes useless.

After the Jaap, one should do Hom (Havan or Yagya) with 1/100 times of the Jaap = 1,250 times

When to Start Purashcharan
Starting of Purashcharan depends on the Deveta you are doing it for. But you can start any Purashcharan in these Muhoort

1. Guru Pushya
2. Ravi Pushya
3. Sarvaarth Siddhi Yog
4. Poornimaa
5. Amaavasyaa
6. Grahan (Eclipse)
7. Nava Raatri
8. Holee
9. Divaalee
but always avoid the Bhadraa Tithi.

Purashcharan
[This whole description of Purashcharan has been taken from "Mahaanirvaan Tantra" by Arthur Avalon, p cv-cvi and other pages. This applies to Devee worship, for other worship it may differ, but it can help understand the meaning of Purashcharan.]

This form of Saadhanaa consists in the repetition of a Mantra a large number of times. The ritual deals with the time and place of performance, the measurements and decoration of the Mandap or Pandaal and of the altar and similar matters. There are certain rules as to food both prior to and during its performance.

The Saadhak should eat Havishya Ann, or alternately boiled milk (Ksheer), fruits or Indian vegetables or anything obtained by begging and avoid all food calculated to influence the passions. Certain conditions and practices are enjoined for the destruction of sin, such as continence, bathing, Jap of the Saavitree Mantra 5008, 3008, or 1008 times, the entertainment of Brahman and so forth.

Three days before Poojaa there is worship of Ganesh and Kshetra-paal – Lord of the place. Panch Gavya (milk, yogurt, Ghee, cow urine and cow dung – the last ones in very small quantity, otherwise they can be replaced by Gangaa water and honey) is eaten. The Sun, Moon and Devtaa are invoked, Sankalp is taken. A Mandal, or a figure of particular design is marked on the ground and a Ghat (Kalash) is then placed on it into which Devee is invoked. The Ghat is painted red and covered with leaves. Five or nine gems are placed on the Ghat. Shikhaa is tied, the posture (Aasan) of the Saadhak is decided, Jap, Nyaas, Mantra etc processes are done. There is meditation. Kulluk (done over the head) is said and the Mantra is awakened (Mantra Chaitanya) and recited a number of times for which the vow has been taken.

[On page 148, Shiv says that "Purashcharan of this hymn of a hundred names (Aadyaa Kaalee Swaroopaa) which is its repetition 108 times, yields all desired fruits." This shows that it s not necessary to repeat something only 125,000 times, a Purashcharan can be of 108 repetitions also.]

--The repetition of the Mantra as vowed for a particular number of times by the worshipper, normally 125,000 repetitions of a Mantra - this practice is called a Purashcharan.
--This is equivalent to 1,250 rounds of a Maalaa in 40 days - 31 Maalaa per day. If somebody takes some 20 minutes to recite the Mantra 108 times, 20 Maalaa will take approximately 7 hours, and 10 Maalaa 3 hours and 30 minutes. Sometimes food and living discipline are also to be followed during the Purashcharan.

(p 151) Purashcharan or Purashkaran means literally "the act of placing in front". By repetition of the name or the Mantra of the Deity, his or her presence is invoked before the worshipper.

In the same reference "Purashkaar" means the singling out of a person from a number and placing him in a position of honor. [Perhaps the Puruskaar word comes from the same root as it also singles out a person from others and places him or her in a honorable position.]

In another example, Devee's Stotra Purashcharan is done by reciting it only 108 times. OR

By another way - There is another mode of performance. A person who, when the 14th day of the dark fortnight falls on Tuesday or Saturday, worships Jaganmayee with the five elements (Panch Tattwa – wine, meat, fish, parched grain and Shakti) of worship and recites with fully attentive mind the Mantra 10,000 times at midnight and feasts believers in the Brahm has also performed Purashcharan.

From one Tuesday to another Tuesday the Mantra should everyday be recited 1,000 times. The Mantra thus recited 8,000 times is also equal to the performance of Purashcharan.

Another View
All Brahmachaaree and Saadhu do Purashcharan. In this, for each syllable of the Mantra, you have to chant the Mantra 100,000 times. If you are initiated into the Gaayatree Mantra, for instance, which has 24 syllables, you have to chant it 2,400,000 times. The Dakshinaamoorti Mool Mantra has 26 syllables so it will take about five years to chant it 2.6 million times, if you chant it about two hours each day. That is why they use the Maalaa to keep count.