Fiji is perhaps a little behind, when it comes to internet options. It's only in the last couple of years that it has become more affordable, reliable, and with faster speeds. Even so, you will find service to be patchy or even non existent in the more remote areas. However, most of the main tourism hubs and resorts have high speed internet, with wi-fi becoming more common. You'll find the service excellent out in the Mamanuca and most of the Yasawa Islands.
There are several internet booths available in the airport (that I'm aware of). For those arriving, go to the domestic terminal, and there is a small internet cafe. Prices aren't cheap, the last time I used it, the cost was fj$5-6 for 30 minutes.
There are also some computers in the departure lounge, for those of you who are leaving. Prices are the same, fj$5-6 for 30 minutes. The slightly annoying thing with these, is how often you purchase a dud card. For me, I found it to be a roughly 50-50 chance. So you have to go back to the shop, wait in line to get it changed, and hope that the new one will work.
Thankfully, the airport does have wifi, so if you have this then you can forget about using the public computers. The wifi covers the whole airport, and will work with any of the pre purchased cards.
All of the main centers have a decent range of internet cafes, with lower prices than you will find at the airport. Nadi, Denarau, Lautoka, Sigatoka, Pacific Harbour and Suva are some of the main centers along the south coast of Viti Levu.
The main resorts all have internet...some of them also have wifi. Not many are free and if they are, you can bet they will be super slow.
Wifi is becoming more common - up until recently your only option was to use the computer in the resort lobby. Slow connection, usually a queue of people wanting to use the single computer, and the costs were ridiculous. This is still the case in some resorts.
There are wifi hotspots all over Viti Levu now, so a standard wifi ability on your phone, ipad etc will probably be enough for you. However, if you want more coverage than you get with standard wifi, either purchase a 4G Flashnet stick, Pocket Wifi or bring one with you. That allows you internet access anywhere that there is mobile phone coverage.
There are two main providers for mobile coverage in Fiji. Vodafone and Digicel. Both provide 4G, which is what you need to connect your laptop/ipad to the internet. Both have an office at the airport, so you can get yourself a sim card and/or USB Flashnet and be setup as soon as you arrive in the country.
My personal recommendation is to purchase a SIM card at the airport from Vodafone or Digicel doesn't matter which. But make sure you get at least 1gb of data or it won't go far. Prices are pretty good now around $35 for data and mobile calls. It's much cheaper and give you loads more freedom than trying to hook into the usually slow wifi at your resort. You can then tether your phone to your ipad/computer to get the internet. Might need a smart phone to tether though. If you buy a SIM with data and calls then you won't need to setup expensive roaming on your phone.
Tip 1: Always get the staff to configure your phone and make sure the internet works before you leave the shop. They are expert at it and will have you up and going in no time. The settings are different and will need to be changed most of the time.
Tip 2: If you don't think that 1gb will be enough for you, then buy extra data when you get the new dongle/SIM car. Don't wait until you are running out to try and find a Vodafone/Digicel shop and go through the hassle of trying to get topped up (speaking from experience).