Learn Hardcore Chinese: wǒ yǒu diànnǎo.

In Mandarin, possession is expressed with the verb 有 (yǒu) “to have/there is,” not with 是 (shì) “to be.” So you say 我有电脑 “I have a computer,” never 我是电脑 (that means “I am a computer”).

Do I need to add “a” (a number and measure word) like 一台?

Chinese has no articles. If you aren’t specifying quantity, 我有电脑 is natural. To emphasize “one,” add a numeral and classifier: 我有一台电脑.

Does 我有电脑 mean exactly one computer?

Not necessarily. It’s indefinite/generic (“I have a computer” as a type). For exact numbers, say 我有一台/两台/三台电脑 or for plural in general, 我有很多电脑.

Which measure word should I use with 电脑?

Use 台 (tái) most commonly (Mainland). 部 (bù) is also common, especially in Taiwan/HK. 个 (gè) is heard colloquially but is best avoided in careful speech. Examples: 一台电脑 / 两部电脑.

Is 电脑们 a correct plural?

No. 们 is mainly for people/pronouns (e.g., 我们). For objects, indicate plurality with number + classifier: 两台电脑, or with quantifiers: 很多电脑.