Before you start breeding. "PLEASE THINK CAREFULLY".
Syrian Hamsters are easy to breed, doing it right is the difficult bit.
What is to happen to the young hamsters, your female hamster will produce. She can have from 6-12 pups per litter
Do you have you an outlet for them. Pet shops normally have a regular supply of hamsters, and will usually stay with his known and trusted breeder / supplier. Most pet shops will not take them from people of the street. Most will only keep a limited number, as hamsters are not babies very long.
Otherwise you could finnish up with a lot of hamsters that you cannot possibly house or keep. It is not easy finding homes for baby hamsters. Even if you try to give them away. This is cruel, and irresponsible breeding.
Syrian hamsters have to be separated into single sex cages at the age of 4-5 weeks, they are capable of reproducing even at this young age.
At the age of 6-8 weeks Syrian hamster will have to be housed individually.
Otherwise serious and persistent fighting occurs. Can you accommodate them, have you got the cages, and space to keep them.

If you are unable to cope, house, and supply the love care and attention that these adorable little creatures deserve then "PLEASE THINK AGAIN"

Oestrus ( "On Heat", "In Season". Period of time when a female hamster will accept mating. ) 6-10 hours (night). Heat generally begins approximately 1-half hours after dusk on the third day of the oestrus cycle and ovulation is completed 6-10 hours after onset of psychic oestrus. If the female is receptive she will quickly assume her position with hind legs spread and tail in the air. If copulation does not occur within 2-3 minutes or if the female becomes aggressive, she should be removed back to her own cage. If copulation does occurs, the pair can be left together until such time as the female shows no further interest in mating. This is usually between 20-30 minutes. or becomes aggressive toward the male. Males should not be left with females for prolonged periods, fighting will occur.

Breeding starts with the introduction of the female to the males cage. The preferred method.
Some female hamsters can be aggressively protective of their territory. Or the mating can be conducted on neutral grounds if you wish.
Once it has been established that she is ready for mating. This should be done about 1-half hours after dark. This is when the female will be at her most receptive time. For the experienced breeder there are many ways in which to do this.
But for the inexperienced breeder one way to do this is gently stroke her back, if she is ready to mate she will go into what we call the receptive pose. That is tummy to the ground, tail in the air.

They can then be left together for about 20 - 30 min's keeping them under constant supervision. During this time after the female is placed into the males cage, the male will start to show an interest in the female. This is the only occasion that she will tolerate another hamster near her.
The male will mount the female for a few seconds only, he will dismount then proceed to wash himself. Then mount the female again. This procedure will take place many times before the female becomes bored of the male, and will then start to become with him.
It is at this stage she must be removed, and return them to their own cages.
If you have made a wrong decision and the female is not in heat, then an aggressive fight will ensue almost immediately. By her attacking the male, separate them try again the following evening.

Once you have let it get to this stage, it is not so easy to separate two squawking Syrian hamsters without getting scratched or bit.
Have a pair of gardening gloves at the ready, or a piece of plastic, or hardboard sheet to obscure the hamsters from each others view until all is calm.
Then return the female to her own cage.