You buy the blasting wand if your doing pretty good and already have a few kills while the enemy team is decently squishy. You buy the catalyst if you have constantly low health. The health potions are for safety when the enemy team surpisingly has good damage.
If you cant afford either just get a health crystal.

Ice shard is your main damage and is a bit trick to use. Try using it whenever your opponent is behind their minions to get that poke but still be out of their range. Her combo is use glacial path in the direction of the champion, click it a second time to teleport as close as possible, use the Ring of Frost to root them, ice shard, ult, and then another ice shard. A amazing initiate that lissandra can do that I only recommend for people with really fast and organized skill using while also having a reasonably high good computer and ping is as follows: use your glacial path to get close to the enemy, and then flash also if need be to get right in the middle of their entire team, ring of frost while ulting yourself, not an enemy champion, and then use the zhonya's hourglass after the ult is over. This allows your team to attack them while they are waiting to be able and attack you while doing reasonable damage.

21/9
Ap with magic resist and armor.

You don't have to follow these if you feel that you have to be a bit more tanky but these are my runes and I like to be able to surprise the enemy in my end game damage. Also the end of the game is usually when you want to do the most damage.

A really fast way to farm the upcoming way of minions is to use Glacial Path at the line of minions approaching and then follow it with a ice shard at the first melee minion. It will usually kill all the minions besides the seige minion when you have the rod of ages and rabadons.