I know that borer is forbidden on Shabbos but if certain conditions are met it may be okay. What are they? 

In a nutshell the melachah of borer involves a mixture of “good” items (objects you intend to use or food you plan to eat) together with “bad” items (objects or foods you don’t intend to use or eat either because they aren’t good or because you have no interest in them at this time).

Selecting the bad items from the good items is considered borer. Selecting the good items from the bad ones is not considered borer and is permitted provided that the following two conditions are met: 1) The good items are selected immediately prior to the time you want to use or eat them; and 2) the good items are selected by hand (or a standard spoon or fork) as opposed to being selected by a utensil that is specifically used for selecting such as a sieve a slotted spoon or a sifter.

My toddler doesn’t like nuts in his salad. How can I pick them out for him? 

You cannot remove the nuts since your toddler views the nuts as “bad” and selecting the bad from the good is considered borer even if you were to do so using your hands or immediately prior to feeding your toddler his salad. One solution to your predicament is that immediately prior to feeding your child you use your hands (or a fork) to remove pieces of salad from the bowl while leaving the nuts behind. Another solution is to pick out the nuts and pop them right into your own mouth.

Occasionally a fly gets into my drink. How can I remove it? 

The accepted solution is to use a spoon to remove the fly together with some of the drink. (Preferably use a larger spoon so that more than a minimal amount of drink is removed.) This is not considered borer since the “bad” fly and (some of the) “good” drink have not been separated from each other; a selection did not take place. Alternatively lift and tilt the cup to allow some of the drink together with the fly to pour out of the cup.

I sleep late on Shabbos morning and my older daughter gets the kids dressed. Can I pick out the kids’ clothing the night before so it will be ready when they get up?

Often picking out children’s clothes will not involve borer. Dresses or pants that are neatly hung in a closet are not considered a mixture and selecting one of them is not considered borer. Even clothes that are neatly piled one on top of the other and are effortlessly separated from each other are not considered as if they are mixed together and you may pick out any garment in the pile.

In some cases when the clothes are not hung up or neatly piled but rather are all thrown together and mixed up (such as clothes in a laundry basket or different types of individual socks that are jumbled together) borer will apply and you may not pick out the kids’ clothing the night before.

I’d like to make a cake platter using only small pieces of cake. If the cake is all the same type just different sizes is it considered borer to pick out the smaller pieces?

No this is not a situation of borer since borer applies only when there is a mixture of two (or more) different types of items. Items of the same type — even if one is big and another small or if one is whole and another broken or if one is thin and another thick — are considered one type and borer does not apply.

If the dried silverware is all jumbled how can I set the table? 

It is forbidden to pick individual pieces out of a jumble of silverware and set them on the table in their correct positions. It is permitted however to do so immediately prior to the meal. For example if the meal is supposed to start at twelve o’clock and it takes about 30 minutes to prepare for the meal then the table may be set at about 11:30 but not earlier. Even if you would like to set your table before going to shul it is forbidden for you to do so.

When the silverware is not mixed together (but is being taken straight out of the drawer organizer) it’s permitted to take each type of silverware and set it on the table in its desired place. But it’s prohibited to take different types of silverware from their individual compartments allow them to mix together in one’s hand and then set them on the table in their correct place. If it’s done immediately before the meal however then this too is permitted.