Learn Swedish: Jag sågade den tjocka brädan själv.

Själv is an emphatic word meaning "myself" or "oneself". It has to agree with the subject doing the action! Since jag (I) is singular, we use the singular form själv. If the sentence were about "we" or "they" sawing the board, you would use the plural form själva.

Can I put själv right after jag, like Jag själv sågade...?

Yes, you can. Placing själv right after the pronoun emphasizes "I myself" even more strongly. However, putting it at the end of the sentence, as it is here, is the most common way to state that you completed an action on your own without help.

Why does the Swedish sentence say den tjocka brädan? Isn't that like saying "the thick board-the"?

Yes, exactly! This is a great reminder of the Swedish "double definite" rule. When you describe a definite noun with an adjective, you must use a separate article (den in this case) before the adjective, and you must keep the definite ending on the noun itself (brädan).

Why does the adjective tjocka end in an -a?

Because it is part of a definite phrase (den ... brädan). When an adjective is used with a definite noun, it takes its definite form. For almost all Swedish adjectives, this just means adding an -a to the end of the base word (tjock becomes tjocka).