In Japanese, たり is a ‘conjunction particle’ that is used in exactly the same way as て. However, instead of having the nuance of ‘then’, or ‘and’, it has the nuance of ‘and things like’. Basically, it is used for listing sequences of events that do not happen in a specific order.
The last たり in any sequence will almost always be followed by する (or した for past tense).

• 休（やす）みの日（ひ）は家（いえ）でテレビを見（み）たり、寝（ね）たりする。
  On my days off, I do things like watch tv and sleep at home.
• 飲（の）み会（かい）で食（た）べたり、飲（の）んだりした。
  At the party, I did things like eat and drink.

From these examples we can see that たり will sometimes be said as だり. This happens with the same verbs that usually use だ for past tense (like 読（よ）んだ), or で for the て form ( like 泳（およ）いで). This will not change the meaning at all, and is only to help make the words easier to say.
To summarize, the difference between て form, and たり is as follows.
Events in order - I did (A) て, (B) て, (C) て, (D) た.
Events in no specific order - I did (D) たり, (B) たり, (A) たり, (C) たりした.
たり is frequently used when there is only one verb in the sentence. This just means that the speaker did ‘things like (A)’, without specifically listing anything else.

• 昔（むかし）あそこの池（いけ）で泳（およ）いだりした。
  In the past, I used to swim in that lake over there. (Among other things)