To expand a bit on what MikeS said, when we think about forces, we mostly think about attraction and repulsion – electromagnetism: like charges repel, gravity: masses attract, strong force: neutrons and protons attract each other. However, that’s not really the whole story – in the case of the strong force, for instance, things only look that easy because the particles involved happen to be colour neutral to an outside observer; internally, a lot more than simple attraction and repulsion happens.
Forces, or interactions between particles, are themselves transmitted via particles. Those force carrying particles can transmit a number of properties according to their own properties – in the simplest case, they transmit merely momentum, leading two particles to either attract or repel each other.
However, that’s only possible if the force-carrying particle itself carries no other charge – take electromagnetism: without going into the subtleties of virtual particles and such, an electron more or less emits a photon that meets with another electron and tells it where to go, and vice versa, leading to a net repulsion between the two. This is only possible in that way because the photon is electrically neutral; if it weren’t, an electron emitting a photon would have to alter its own charge, since charge is conserved (i.e. it would have to give a bit of charge to the photon it sends off), thus becoming a different particle.
That’s basically what happens in strong interactions: quarks carry a type of charge, called colour, and so do the force carrying particles they exchange, the gluons. Thus, whenever quarks interact via the strong force, they change their own colour according to certain rules, causing this nice and tidy Feinman-diagram of nucleons interacting via the exchange of a (virtual) pion to become this considerably more tangly and messy representation when one looks at the internal processes going on.
Yet, quarks of a different colour are still quarks; the weak interaction is mediated by particles which may carry electric charge, +1 in the case of the W[sup]+[/sup], and -1 for the W[sup]-[/sup]. This leads to a wholly different kind of change, and here’s where beta decay comes into play: beta decay, or rather beta-minus decay, is a neutron decaying into a proton, an electron, and an electron-antineutrino, n -> p + e + 'v[sub]e[/sub].
But, looking at the messy insides, what actually happens is the conversion of a down-quark (which has the electric charge -1/3) into an up-quark (charge 2/3) via the emission of a W[sup]-[/sup], which then decays into electron and neutrino, corresponding to a Feynman diagram like this; you can see how the (electric) charges add up: 2/3 - 1 = -1/3.
Thus, in this case, there appears to be no attraction/repulsion going on, since the particles in question change; however, that’s due to the particulars of the force-carrying particles, otherwise there’s really no distinction from the other forces.
But, as MikeS already pointed out, there is a way in which the weak force behaves exactly like our more everyday notions of ‘force’ would have us expect. This is due to the fact that, besides W[sup]+[/sup] and W[sup]-[/sup], there’s another force-carrying particle associated with it: the electrically neutral Z (sometimes called Z[sup]0[/sup], but I’ll spare myself the coding).
Now, this thing is essentially a heavy photon – really heavy, in fact; all the weak force carrying particles are basically the lard asses of the particle zoo, weighing more than individual atoms, which is also why they don’t usually get very far: mass is correlated with half-life, and those little things decay really quickly – and thus, a bit hard to observe: all interactions between electrically charged particles that can be accomplished via (virtual) Z boson exchange can be more easily accomplished via photons, so, one needs to look at electrically neutral particles, i.e. neutrinos. There, Z boson exchange leads to elastic scattering, which is pretty much the transfer of momentum I have earlier equated to our everyday attraction/repulsion notion of force; the existence of this ‘neutral weak current’ has been experimentally confirmed in 1974 at the Gargamelle bubble chamber at CERN.
So, put simply, the confusion about the weak force behaving strangely doesn’t really originate with the particulars of said interaction, but with our everyday notion of force being rather incomplete when it comes to particle physics – beta decay is as much the result of a force, or rather interaction, as two electrons repelling each other is.