Hamsters normally reproduce sexually. A boy hamster meets a girl hamster and falls in love, and after a proper period of engagement they marry and have babies - a process that involves both the boy and the girl hamster, and results in children that are a genetic mish-mash of the two parents.
This mixing up of the genes thing is designed to increase genetic variation within the community and therefore make it stronger (i.e. so a particular disease doesn't wipe out all your hamsters because they all have the same genetic propensity to get it). It's also designed to basically just jiggle everything around a bit to see if a better combination of genes can arise...thus helping hamster evolution along as well.
Of course, sometimes girl hamsters just don't meet Hamster Mr Right. Until recently, they still had a plethora of options open to them of course - adoption, artificial insemination, one-night stands...however thanks to recent scientific breakthroughs, they also now have cloning.
In principle, it's dead easy too. First, get a cell from the poor on-the-shelf hamster that can't get a bloke, and culture it for a bit. This has the effect of "switching off" the cell's identity - so for instance, if it was an ear cell, it would just become a homogenous blob in a petri dish. If it was a tail cell, that too would become a homogenous blob in a petri dish. Its as if, as soon as you put any sort of cell in a petri dish and make life easy for it, it starts eating lots of nutrients, really letting itself go, and can't be bothered to stay in shape any more.
Then, once you have a nice fat "switched off" stem cell from your on-the-shelf hamster - get an unfertilised hamster egg. Stick a very fine hollow glass needle into this egg and suck out the nucleus (the black bit with all the DNA in it - you can't miss it) and chuck it away. This is called "enucleating" it, and all that should be left is the cyctoplasm - the jelly bit - at the end of it.
Finally - put the fat "switched off" cell and the enucleated cell in a fresh petri dish - and pass an electrical spark through the medium to encourage them to fuse (its not quite as romantic as sexual reproduction, I'll grant you, but it works and it has a nice name too - "electrofusion"). Culture the hybrid cell for a bit - then slap it into another hamster that's happy to suffer stretch marks and take a few months out of its working career - and sure enough Bob's your Uncle (and simultaneously your great uncle as well). The theory is that Dolly the hamster will grow up with the same genetic make-up, weaknesses, strengths, and irritating little habits as its on-the-shelf Mum. Mum doesn't need a long term partner any more, she can continue dating bloke hamsters that don't want any commitment - and everyone is happy.
The fact is that though Dolly the hamster will share most of its genes with its wayward Mum, it will probably have got around 20 genes from the cytoplasm of the anonymous and selfless hamster donor of that egg that got its nucleus ripped out. It will probably also have upwards of 50,000 genes from its surrogate Mum as well. So what you have done with Dolly is just done a partial clone - but that, as yet, is as close as we can get it. At least it will have its mothers eyes...
Oh yes, I forgot to mention. You might need around 277 electro-fusions, 247 oviduct-cultured embryos and 29 embryos transferred to about 13 hamster wombs in order to get one successful Dolly. So save up before you start.
Ah...and...you might also want to pause to consider the deontological ethical position which gives moral value to the telos or essence of hamsterness. In terms of hamsters running round wheels, stuffing their little cheeks with food and walking of the edges of tables, the hamster telos is clearly violated here. But falling back on a utilitarian or consequentialist ethical position - can inflicting all sorts of biotechnological procedures on hamsters be justified in terms of the consequences, e.g. giving rise to a new transgenic hamster that can talk, present tv programs and do its own shopping? Considering all the experiments I have already performed on our furry little friends, I think I've made my own stance clear enough - but you...you might want to keep the location of your lab anonymous and not get into any religious debates for a while...