Genki explains it something like this:
You can use the te form to link two verbs:
e.g. 東京でテニスをして、ビールを飲みます。
In Tokyo, I will play tennis and drink beer.
But this sentence implies that playing tennis and drinking beer are the only things you will do, and also that you will do the things in that order.
The たり… たりする construction can be used instead. This construction implies that these are examples of things you will do, rather than a complete list. It also doesn’t imply they will be done in a set order. So it means: I will do things like A and B.
e.g. 東京でテニスをしたり、 ビールを飲んだりします。
In Tokyo, I will do things like playing tennis and drinking beer.
To make the たりform you just add り to the –た form of the verb (i.e. the informal past tense).
Examples:
する: -た form is した；-たりform is したり
飲む: -た form is 飲んだ；-たりform is 飲んだり
And in our text:
もらう: -た form is もらった；-たりform is もらったり
およぐ: -た form is およいだ；-たりform is およいだり
On the end of the construction we put the appropriate form of する– in my example the polite present します.
So the overall construction is:
(predicate/activity A)たり (predicate/activity B)たり する。
That was useful revision for me! The examples are my own. I spotted one error when I was checking so please let me know if you spot another!