Updated to use DM Basic Rules v0.3 (same method used in the DMG) on 2015-02-15
First, fill in the number of characters in your party and their level. If characters in your party are at different levels, add multiple rows and include each group of characters with the same level in their own row. Next, press CALCULATE to see the encounter XP thresholds for the party.
For example, if you have four first-level characters, type 4 in number, and 1 in level. If you have three seventh-level characters and one eighth-level, type 3 in number, 7 in level, add a second row, and add 1 in number and 8 in level.
Second, fill in the number of monsters and the amount of XP that each one gives in a similar manner. Finally, press CALCULATE to see details about the encounter, and to get a difficulty rating for the encounter given your party.
Alternatively, check the "Use Challenge Rating (CR)" box, fill in the number of monsters and the CR for each monster rather than its XP level.
First, congratulations on running a game! You'll get the hang of it pretty quickly. The easiest way to build an encounter is to pick an enemy from the Monster Manual with a CR around the same as the level of PCs in your party, maybe one higher if you want them to have a tough fight. This won't always be perfect, but it's a good place to start. You'll find that this method mostly generates Medium or Hard difficulty encounters, which is about what you are aiming for.
To spice things up, increase the number of enemies. Either go for a group of lower-level mooks, or a second bad guy of around the same CR, or mix and match. Don't go too wild with this, though - the PCs can only take on so many enemies at once. In 5th Edition, outnumbering your opponent can be quite an advantage. Be very careful before putting your PCs up against a Deadly encounter, especially against lots of enemies.
If you're using this calculator a lot, you may have found it can seem to overstate the difficulty of encounters. First I'll explain why this happens, and then how you can fix this.
The biggest culprit for easy encounters is the party resting too much. If you're like me, your parties tend to have maybe two or three encounters per long rest, often with short rests in between - this makes more sense for some play styles, but causes balance problems.
The way 5th Edition balances resources assumes that parties will have at least a couple of medium-difficulty encounters between each short rest, and maybe two or three short rests between each long rest. This forces characters to be conservative with their limited resources (spell slots, class features, hit dice, and so forth), making each individual encounter tougher. A party that can approach an encounter fresh, with no worries about saving resources, will often find that encounter relatively easy.
How do you fix this? You have two choices.
*Note for those who use CR, this scales differently. You may only want to increase the CR of encounters by 1 or 2.