The Ritualist works in a few main way really. To beef up your party with weapon spells, to help your party with restoration spells and spirits, to cause some pretty good AoE damage with channeling magic and to create a good deal of spirits and using spells to spread out and increase their damage.
Spirit Spamming
Spirit Spamming is the creation of a lot of spirits and to increase their damage in a short amount of time. A few good spirits to ALWAYS bring are bloodsong (factions) vampirism (nightfall) and as an elite wanderlust (factions) thes three are important but don't forget painful bond (core) it makes every spirits attack add X damage.
There are two ways of setting spirits, one is what I call a “Spirit Stack” where you pile spirits together in one place. This is faster for creating spirits but doesn't work so well if you are fighting something with AoE damage or something tat likes to get spirits first before players.
The other way is to create spirits in different locations (usually circling the target(s)) this is a bit slower but it is less likely that all of them will be killed, this is better against enemies with AoE damage or a large group of enemies which may take longer to kil all of them.
Weapon Spells
Having a Ritualist with weapon spells can really help your party anywhere. A few good spells to keep would be brutal weapon (core) weapon of warding (core) and an elite weapon spell.
You usually want to set up the longer lasting spells just before you fight a group. Make sure to place defensive spells on the casters and heavy offence spells on the warrior, dervish, assassin, and ranger.
While fighting a group though watch for when the weapon spells wear out and recast some short-term spells just for the moment.
Lightning Spike
I don't personally use Lightning build much but I know the dynamics of it.
The Lightning Spike build is mostly used for solo farming as it has good AoE damage and really packs a punch. When you are creating a lightning spike build it is pretty well free as to what you use but keep in mind you want to bring some heavy AoE spells and maybe one good target skill to mop up any survivors a good one to bring would be spirit rift and channeled strike isn't too bad for taking care of any survivors.
When you are doing solo farming with this build you will probably want to bring a tanker hero and get him to attract a group while you hide and then take them out from a little ways away.
Restoration Ritualist
A Resto Rit is really just a hybrid of a spirit spammer and a weapon spell Ritualist all you have to do is use a few good healing weapon spells like weapon of warding and some restoring spirits like recuperation.
Keep in mind that while you are laying down spirits or casting weapon spells just try to stay well out of the way. The great thing about effect spirits is that they can work from a fair ways away so you can flag your party in the middle of it all and work on the sidelines and watch your party do all the fighting.
Minion Bomber
The minion bomber is actually a Ritualist Necromancer build but it was so great I thought I just had to add it.
A minion bomber I like better as a Ritualist necromancer build because a necromancer CAN do it as a necro primary but the Ritualist does it with more style. The whole idea behind it is QUANTITY QUANTITY QUANTITY you need to have lots of minions so use animate bone minions and animate bone minion that and for the bombing part us explosive growth and death nova. You can spice it up with a little bit more but that is the basic idea.