The main source for both battles is The Histories by Herodotos of Halikarnassos. Herodotos was born around 480 BC, the year the battle of Salamis was fought, but he was still able to talk to eyewitnesses to compile his accounts of Marathon and Salamis.

In the case of Marathon (Hdt. 6.103-114), his work is also the only source describing the event. All we have besides that is monuments (or descriptions of monuments that don't survive) and the finds from the funerary mound raised on the battlefield.

Salamis is a bit more complicated. We have a more contemporary source than Herodotos' account (Hdt. 8.56-95), in the form of the tragedy The Persians by Aischylos, which was first performed in 472 BC. It contains a lengthy and detailed description of the battle (Pers. 353-472). Aischylos' gravestone records that he fought at Marathon, and he may well have fought at Salamis too. On the other hand, his work is not history but tragedy. The extent to which he cared to describe events accurately is unknown.

Aischylos' version of Salamis puts much less emphasis on the role of Themistokles, and much more on the role of Aristeides and the assault on the island of Psyttaleia, where the Persians had set up an outpost. It is not clear why he felt this was more worthy of his attention. It's most often assumed that Aischylos wanted to represent the infantry action of the wealthy, rather than the rowing action of the poor, as decisive.

For what it's worth, the much later accounts of Diodoros (11.14-18) and Plutarch (Life of Themistokles 10-15) essentially summarize Herodotos, and agree with him on Themistokles' decisive contribution.