Correct. The smaller the Ka of an acid, the weaker the acid is. The smaller the Kb of a base, the weaker the base is.
Now for what your textbook says. When you look at a Ka or Kb value, it's really just an equillibrium constant stating what the concentration of the undissociated and dissociated acid/base will be at equillibrium. If you have a weak acid, like acetic acid, the small Ka means that at equillibrium, you will have more undissociated acetic acid in solution than you will acetate and hydronium ion. Now look at the salt sodium acetate. It is composed of the conjugate acid of a VERY strong base (NaOH), and the conjugate base of a pretty weak acid (Acetic acid). So when it goes into solution, the equillibrium between NaOH and (OH- + Na+) will be favored towards the Na+ and OH-. There will be no formation of NaOH. For the acetate part of it, the equillibrium constant will favor the formation of acetic acid and not acetate and hydronium ion. (I.E. there will be more CH3COOH in solution than there will be H+ and CH3COO-). So when it's all at equillibrium, the acetate ion would rather be in the form of acetic acid. Therefore, it will pull an H+ off of water leaving both items in their equillibrium favored state. (The CH3COO- as CH3COOH and the Na+ as Na+ and OH-). Therefore, the presence of the OH- ions makes the solution basic. The reverse can be applied for bases. If you have NH4Cl, you have the conjugate acid of a weak base (NH4OH) and the conjugate base of a strong acid (HCl). Therefore, at equillibrium the conjugate acid would rather exist as the undissociated base (NH4OH) than it would as the conjugate acid (NH4+). The conjugate base would rather exist as the conjugate base than it would the undissociated acid (HCl). Therefore, it will remain in solution as the H+ and Cl- ions. As a result, the solution is acidic.
The conjugate acid of a weak base really wouldn't be considered a strong acid since when put into solution, it doesn't completely form the weak base and H+ ions. A small bit of it does, but not a large amount. Therefore, it would be considered an average acid. (Please correct me someone if I'm wrong). What determines if an acid/base is strong or weak is the completion of its dissociation. An acid/base that completely dissociates into its ions when placed in an aqueous solution is considered a strong acid/base. Therefore, you can go by it's Ka/Kb value. Sodium hydroxide, when placed in water, is pretty much 100% dissociated. Therefore, it's considered a strong base. The same can be said for hydrochloric acid. There is an exact number for the Ka/Kb that can be used, but I can't recall it off the top of my head. (Also, please note that for sulfuric acid the acid is considered a strong acid but only for the first hydrogen. That is, when placed in solution H2SO4 will completely dissociate into HSO4- and H+. But the HSO4- is a weak acid and only partially dissociates into H+ and SO4-).