How do you know if the product in a chemical equation will be aqueous or solid?

No way to tell for sure, you just have to go with some known guidelines. Light hydroxide compounds like NaOH or LiOH might be aqueous, but when you have a heavier element in the OH group you will get precipitates which are solids. CaOH and MgOH BaOH fall into this category.

Same thing with the chlorides. NaCl will be aqueous, AgCl won't be.

So look for groups which easily mix with water , which will be the halides, alcohols and hydroxide (OH groups) . The other half of the compound is more related to a heavier atomic mass. Lead is heavier than sodium, so lead compounds will precipitate, sodium compounds will be aqueous