For current weather conditions, this link to Weather Underground gives you fairly accurate information for Accra.
For historical weather, this link to BBC is very helpful.
Ghana enjoys a year round tropical climate, but it does have rainy seasons. The coastal region (including Accra) has two rainy seasons, one beginning in March, and peaking in May or June, the other in September/October. Even during the rainy season, Accra can still enjoy an average of 5 hours a day of sunshine. During this period, the rain tends to be the result of increased heat and lowering barometric pressure, in other words, thunderstorms. They are typically of relatively short duration, but can be exceptionally powerful, resulting in localized flooding. Average temperatures along the coast are usually in the 23-31 Celsius range (or in Fahrenheit, between say 75 and 90 degrees) . In the north part of the country, there is a single rainy season starting in May or June. It tends to be significantly hotter as you go further north, as the coastal breeze keeps the temperatures down.
An interesting phenomenon occurs beginning in December or January, known as the harmattan. That is a dry and dusty wind blowing south off of the Sahara desert into the Gulf of Guinea. The heavy amount of dust in the air can severely limit visibility and block the sun for several days, comparable to a heavy fog. At night time, in the beams of a car's headlights, you can actually see the dust in the air. It gets into and onto everything, even a closed house will become dusty inside as it seeps through the screens and under doors; outside you can see the fine yellow silt covering the cars. Naturally, it is a health hazard, as incidents of asthma and other breathing difficulties increase significantly during this period. Another less common malady is harmattan eye; the eye becomes red, oozes puss, and becomes swollen as a result of the minute particles getting under the eye lid. You won't even feel the irritation, bit you will wake up looking as if you'd gone a few rounds with Mike Tyson. If you visit Ghana during this period, bring a good moisturizing skin lotion, moisturizing eye drops and don't forget lip balm.