"Please read the letter immediately."
If you’re asking me, both are correct. However, there is much more of は than it seems on the first glance. In this example, the sentence literally can be translated as “As for the letter, do read immediately.” This indicates that the speaker wants to talk about the letter.
読む is a transitive verb, so the normal way to say "please read the letter" is "てがみを読んでください”. But here は particle is used to emphasize topic and literal translation of てがみはすぐに読んでください may look like "Speaking of letter, read it immediately"
In the topic-comment structure, although our attention is being drawn first to the topic, it is the following comment about the topic which is the new, and therefore emphasized information, not the topic.
Not only grammatical subjects, but also direct objects can be made into topics. So you might say that the underlying particle is を, but if the direct object is made into a topic, you will use は instead.
読む is the plain non-past form, that corresponds to the polite form 読みます, built on 読み. 読む is also the basic dictionary, or citation form, for looking the verb up in a dictionary. 読んだ is the plain past form, that corresponds to the polite form 読みました. The verb 'yomu' is a consonant stem (godan) verb, for which the stem is yom-: -u is added for the plain non-past final form (shūshikei), -i for the continuative (ren'yōkei), -a for the negative / 'imperfective' (mizenkei). Joined with a following て or た, the m at end of the stem assimilates (merges), adding voicing, resulting in で だ. Hence, 読んで (the progressive or command form used with ください) and 読んだ (the plain past form). The resulting forms may in many cases be further combined to produce additional forms.
A few examples: From 読み: 読みたい want to read, 読みながら while reading, 読みにくい difficult to read.
From 読ま: 読まないで (negative command form used with ください ...), 読まなければ (if one doesn't read).
There's a neat little graphic in the Wikipedia article on Japanese Verbs (https://en.m.wikipedia.org/wiki/Japanese_verb_conjugation) that you can download too, if I haven't already overwhelmed you with you much info. :-)