Your life from level 1 to 5 is very simple, and provides a good chance to get a feel for what it's like to play a caster. You will notice very fast that you are not melee-oriented, and cannot last long in direct combat. It is however possible to fight hand to hand at this early level, and it's a good idea not to get used to that.
Basically, your attack method is to cast your offensive direct damage spell on a monster from max distance, and repeat quickly before it reaches you. You can hold down the hotkey that you've assigned for it for a quick rapid cast, or click furiously on the spell icon. You should have no problem getting 3 casts off before the monster reaches you. When it does, it's time to finish it off with your staff. You will be unable to cast anymore spells while being attacked, so the key is to do as much damage as possible before that happens.
Stick to monsters that con blue and green to you, don't get cocky just yet. You will have no trouble soloing higher con monsters later on, but until you actually become a Theurgist, your power is limited. Be sure to check your spell list every time you advance a level, as you will learn more powerful spells often. Always keep that crystal shield on, as it is our version of armor. In short time, you will be level 5, and ready to move onto bigger and better things.

Path of Earth

These spells are primarily for buffing. They include your crystal shields, and earthen bursts. Your shields will add AF (armor factor), and are self only. They are our only true armor, and should be kept up at all times if possible. Earthen bursts are terrific attack enhancers, and will increase the output on melee greatly. Tanks will welcome this buff when you are grouped. Both of these spell lines simply increase in effectiveness as they get higher.

This is the specialized Earth line, and will only be increased if you add spec points into it. As of right now there is a bug where you will not see any spells in this line until you get it to level 5, so do not panic if you aren't recieving new spells at first. Your abrasion line includes your earth elementals, skins, and attack speed debuffs. Earth elementals have the highest amount of HP and attack damage, and also last the longest. They are your tank elementals. Skins, also referred to as bladeturns, are probably the most important spell you will get when you begin to RvR. It provides whoever is wearing it to completely absorb a physical attack, of any strength. Although the casting time is longer, there is no limit to how many times you can cast a skin on someone. It is possible to make someone almost completely invulnerable to melee attack with your skin spells. Your Friction spells are your attack debuffs, and cause the target to hit less frequently, thus reducing overall damage over time.

Path of Ice

These are your basic direct damagers, and root spells. Your ice nukes will increase in damage and effectiveness with each new line, and your roots will last longer and land more often without being resisted. For those that don't know, a root spell refers to a spell that holds an enemy in place until it is either damaged or wears off.

Refrigeration is the specialized Ice line. As with Abrasion, a current bug prevents any spells from showing up until you have 5 points into it. Refrigeration includes your ice elementals, a different type of ice nuke, and an area of effect snare. Ice Elementals are your caster elementals, they will attempt to keep enough distance between them and the target to send ice nukes at them. These ice nukes will slow running speed as well as damage. If the target comes into range, they begin melee, and are not good at it. They also have very little HP, and die quickly. Ice Blasts will do the same damage as Path of Ice nukes at their appropriate level, but also will add a slowing effect, much like the nukes your ice elementals cast. This can be good for slowing the enemy down in order to get more blasts off before they reach you. An impressive sight is the area of effect snare. Your Ice Field spells will snare the targetted enemy, as well as those around them, bringing their movement almost to a complete stop. It will wear off slowly, causing them to regain their speed a little at a time. As the levels increase, your snare range will get larger, and the snares themselves will last longer.

Path of Air

Your Path of Air spells include a melee haste spell, and a running speed increase. Storm spells are short duration hastes, that when cast on someone, will increase their rate of attack, and cause them to land more hits as well. Wind spells increase running speed, and affect the whole group when cast. However, they are not active while in combat.

Vapormancy is the specialized version of the Path of Air. These spells include your air elementals, a powerful direct damage spell, and an area of effect mezmerize. Air elementals are considered the all around average of the 3. They have about half the HP of an earth elemental, and do about half the attack damage. However, they have the ability to land short duration stuns on their target, which can be helpful in delaying your target's time to reach you. The one downfall to the air elemental is it's duration, the shortest of the three, at 20 seconds. Your Blasting Wind nukes are by far the most powerful of all the direct damage spells you can get. They do half again as much as your regular ice nukes. Confusing Gusts are your area of effect mezmerize spells, and like the AoE snare, will increase in range and length as they get higher in level. Mezmerize will render a target unable to move, or attack, but for a shorter duration then a root or snare spell.

Many would agree that the Theurgist makes the best soloing class in all of Albion. This is because we can utilize our pets in such a way that we can create our own group for us. Earth and Air elementals can do the tanking, while Ice elementals blast from a distance. Of course, since all our pets are of short duration, we need to cast several to get the job done. Elementals can be cast from a great distance, farther then nuking range. Your typical method of attack will be to send out your strongest type of elementals, back up a bit, and finish with direct damage spells if the enemy survives long enough to make it into your range. Elementals that time out or die will pass along 1/2 of all their aggro onto you, so once you've sent a few pets, it will be very hard to get that enemy off of you. Be aware that when one of your elementals is in combat, it considers you to be as well, so your running speed increase will not be in effect. If things aren't going too well, run early. Your elementals that are still pounding away at the monster will continue to do so as you flee, and if you are lucky, will finish the job for you or weaken the target enough so that you may turn and blast them dead. Remember, enemies that have below 1/5 of their life remaining move extremely slow, and are easy prey.

Because of our ability to summon many pets and let them do the fighting for us, it is easy to take down orange, and sometimes red cons. It should be known that many Theurgists have died trying to be conservative. Do not underestimate your opponent if they con orange or red to you. Send out that extra pet and don't try to cut it so close. A few extra seconds of sitting to recover that little bit of power is much preferred over dying, because you wanted to conserve.

After level 20, it is ill-advised to attempt melee AT ALL, no matter how close the monster is to dying. We miss often on yellow and above cons, and they hit very hard. If a monster is close to you, it may seem to have an additional reach while you back away from it. If the monster is almost dead, and you are out of power, a simple method is to just back away for a bit and rest quickly, to recover enough power to nuke them once and finish them off. Don't get too far away though, or the monster will begin to flee, and may stay out of your range wisely. You will then find that later on, when you least expect it, that monster will return to wreak havoc on you at full health, while you are fighting something else. That is another reason NOT to be conservative when soloing. Do what you can to defeat what you're after, don't hold back.

Theurgists can solo all the way to level 50, though it gets slower. After level 25, it gets much harder to kill oranges, and sometimes impossible to kill reds. All monsters are different, so experiment with the ones that you can handle safely.