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How do we price credit risky bonds?
If I discount the cash flows using LIBOR/zero rates, it won't take the credit riskiness into account. So should I use a rate based on the issuer's credit spread? Or is there a separate way to price in credit riskiness (maybe using default probabilities)?
Normally, you do indeed add a credit spread $s$ to the risk-free spreads to price the bond. That is, if the coupons are $c_i$ at times $t_i$ and the notional is $Y$ then you price it as
$$ R\!B(t) =Y \exp{\left( -\int_t^T s(x)+r(x) dx \right) } +\sum_{i \ni t_i>t}^{N_c} c_i \exp{\left( -\int_t^{t_i} s(x)+r(x) dx \right) } $$
Normally you have too little information to incorporate a term structure for $s$, so you just make it some constant $s_0$. Once in a while you have enough information from other bonds or credit default swaps to determine a term structure.
