Firstly, internet speeds in Sierra Leone are nothing like in the developed world unless you happen to have access to private VSAT. Prepare yourself for painfully frustrating speeds. The main hope for Sierra Leone's long suffering internet using public lies in the fibre optic network which is expected to come live in the latter part of 2012. Till such time there are some options available.
VSAT through Satellite Providers
This is an option that only the bigger companies would be able to afford. For a high end 1mb package, this can cost over $5,000 a month whilst the lower end for business would be around $1,000 per month. Companies providing this service include AFCOM, Limeline, IPTel and others.
Airtel offers 3G services or according to them "3.75G" to be precise. You can purchase a modem (USB stick) for around $70 which can be "topped up" much like you do with phones. 12,000 units (1000units=Le42,000) will give you 3GB data but there are cheaper options available. The more data you subscribe to, the cheaper the cost per unit.
As Airtel charge based on data consumed, you might want to make sure you don't have services running in the background without your knowledge (Windows Update for example) otherwise, this will cut through your data quicker than you would believe.
To be fair to like Airtel, when it works it's the best option I found out there for mobile providers. I have however found it to be location dependent, as the 3G towers are not everywhere so you might want to test before you invest in a modem. Airtel is also a great for smartphones and have good coverage out of Freetown.
Africell also offers 3G service and claim to be the quickest 3G provider in Sierra Leone. They currently have a promotion being run and it is free until they officially launch. I have also used this, but found it inconsistent as the connection was dropping a fair bit. This would not be ideal for business use. They also do not have a modem, you have to pair it to your laptop in order to be able to access the internet from your computer. If you only need the internet for fun and mainly on your phone, then Africell may be an ideal solution for you, particularly as it's currently free.
Comium (WIGO) offers internet through a USB device and for $70 per month you can get decent speeds. Their device is not as portable as Airtel or Sierratel's. Internet through your mobile phone is only available to post-paid customers and it is not 3G.
Sierratel offers internet through CDMA modem. They are not the fastest but their connection is often stable but their coverage outside Freetown is not as good as with Airtel.
Hotels and Restaurants
Some hotels and restaurants offer wireless internet service and it may be possible to use these but probably not a good idea to make a habit of it. Some may charge whilst others would rather you buy a meal from them. For example, Taia Resort charge $5 for 2 hours where as the Country Lodge requires you purchase food from the restaurant. Family Kingdom and Sierra Lighthouse also offer wireless internet. See other hotels with wireless internet. A popular restaurant where you can get internet access is BLISS on Wilkinson road. They currently charge Le10,000 per day which is pretty good as the internet speed is very good. It is advisable that you purchase food from the restaurant as well just so you can seat easy.
There are internet cafes all over the city offering access on an hourly basis and this is probably the cheapest option. You would however want to keep in mind that most antivirus software in Sierra Leone are out of date and catching a virus is very common. For this reason if you could take your own laptop to the cafe, it would be the best option. If you want your privacy then one of the mobile providers would be the way to go.