I'm afraid I know of no strategy for recognizing silent letters easily. But three hints may be useful:
First, some silent letters serve diacritic functions: The silent final <e> in gate marks a long vowel, and the silent <u> in a word like guest keeps a <g> from looking as if it should be pronounced [j] rather than [g].
Second, many silent letters are due to simplification of the way words used to be pronounced, so the more aware you are of other words that are historically related to the word with the silent letter, the easier it may be to recognize that silent letter.
And third, in a few cases a letter falls silent only in specific settings -- for instance, the way <d> falls silent between <n> and a following consonant, as in hands and grandfather.
Beyond that, it is pretty much a matter of brute memorization.