Joensuu has a small airport and you can get there by plane at least from Helsinki.
Train and bus transportations are available from (almost) all over the country but you won't probably get a direct connection if travelling from western or northern parts of Finland.
You can also get to Joensuu by car, motorbike etc.
If you are staying at the city center you can go everywhere by foot. There are some local bus lines in Joensuu if you need to get outside of the city.
If you have money, the best way is to fly from Helsinki to Joensuu. If you are on a low budget, you can take a train from various towns to Joensuu. From Helsinki it takes five hours by train to Joensuu.
Joensuu is a small town which is very famous of its cycling routes. Actually you can walk almost everywhere.