Hard to spell words can be frustrating for kids and adults alike. The English language, for all its beauty, is capricious and fickle.

Just when a "rule" is learned, such as "I before E except after C" there are exceptions put in: "or when sounding like A as in 'neighbor' and 'weigh'." Then, some aspiring novelist decides to put in a sentence like "Neither of the foreign sovereigns wanted either of the feisty heifers for protein, and they seized the weird kaleidoscope from the counterfeit poltergeist!" and the rule goes up in a puff of smoke.
Unfortunately, the best way to learn hard to spell words is the old-fashioned method of rote memorization. The process of imprinting the actual spellings of unusual words past the short-term memory into long-term storage has thankfully moved beyond the days of sitting at desks and simply repeating the letters over and over. Several mnemonic training techniques used by champion spellers the world over can be utilized to train anyone to be a master speller.
Many of these utilize the concept of kinesthetic learning. Associating a mental concept with a series of movements – almost like a dance – can help hardwire the series of letters into the brain much more quickly and durably than repetition alone.
One of the easiest ways to come up with that series of movements is to simply have the learner trace the letters into their hand as they are saying the letters out loud. This will reinforce in three kinesthetic ways: with the motions of the mouth and lips, the fingers of one hand moving, and the feeling of the motion on the other palm.
Larger body motions can also be used to learn and remember correct spelling, which makes learning a much more active experience. Among other things, the large motions stimulate the blood flow to the brain, making it more receptive to the learning process.
Sessions of studying like this will be more effective if they are done in small bursts of time, with breaks to give the mental palate a time to refresh and ready itself to ingest the next set of words. "Cramming," especially before a test can be counterproductive. It can also increase the chance of reinforcing mistakes.
Of course, it takes more than one repetition to come close to imprinting the correct spelling. The word should be repeated many times, like a drill, until the motions and the sounds almost lose their symbolic meaning. Divorcing the sounds from the meaning, turning them into a song of sorts, can also work well as a strategy. Saying "Ex-a-cer-bate" syllable by syllable makes the brain identify the sections as individual pieces each of which can be spelled correctly. The repetition of the sounds becomes melodic, triggering auditory learning skills that are developed from childhood through nursery rhymes.
This leads to another strategy for learning hard to spell words: learn them in groups that follow similar patterns. In the sample sentence from the first paragraph, all of the words with "-ei-" combinations follow the same pattern. If all of them are learned at the same time, they will become associated with each other and reinforce the correct spelling. Whether in a simple list or through a sentence (no matter how nonsensical), rolling all the similar spellings into a group helps to both categorize and memorize.
Even using these tools, memories can fade and become confused or conflated with new vocabulary. One of the best and most-overlooked techniques for learning both grammar and hard to spell words is simply reading – a wide variety and as much as possible. The more times the eye sees words spelled correctly, the more easy it is to spot mistakes. It becomes less a matter of following rules as much as gaining an intuition as to when a word simply feels "wrong."
Whatever the technique used, you can find words to study at yourDictionary's list of the 100 Most Common Misspelled Words. Aside from being a comprehensive list, it also has many more mnemonic techniques for learning the correct spelling of specific words. With these tools, spelling becomes a matter of habit, rather than a puzzle, and writers can concentrate more on the message they are trying to convey.