This is a problem all of us in the modern world face - using our phone abroad without racking up a superbill that wastes away precious money and time. Nearly all our phones are smart now so there is always a way to stay in contact with your friends & family without using your normal contract.
Start by turning your data roaming off. This is the classic mistake that many of us can easily make. We hop off our flight, turn our phone off airplane mode but with roaming still on your phone keeps downloading messages that builds up your bill. Who needs roaming when every other cafe and tourist centre has wifi these days anyway? We're addicted to our technologies these days but you don't have to be, you can last that 10 minutes from leaving the cafe wifi to getting back to your hotel or hostel. However, if you realllllly can't survive without there are a few low priced options for you.
You can get a SIM card in the country you're staying in. They'll try to sell phone packages to your at the airport but walk straight on by as they're a rip off aimed at overcharging tourists like us for services we don't need. Wait until you get into town and head into one of the many shops that will sell SIM cards, or ask your accommodation as many give out the SIM card for free and you can top up credit while you're there. This is a really great option if you need to make some in country calls such as to a tour provider to book your next leg of the journey.
You can also purchase a roaming package from your provider at home before you leave. Some of these I don't rate at all so do your research before you agree. I had a great one from EE before when backpacking through Europe. I could use a load of data for £1/day but if I didn't use data that day I wouldn't be charged. There a whole range of these sorts of deals from all the network providers so just do some research and ask around to find something that will suit your needs best.
Also be aware that some of your tablets are using mobile data and are contract, if yours is on contract do the same and turn off data roaming or get a package to cover your use abroad.