Well,you have to follow the recipe for the particular beer style you're brewing,1st of all. It's typically the times they list that are incorrect. But,basically,for apartial boil;
1) Get 2.5-3 gallons of water boiling in at least a 5G brew kettle. Preferably stainless steel. On my electric stove,that's wide open.
2) While that's getting going,measure out your hop additions into bowls &/or hop sacks/grain bags. Depending on pellet or whole leaf.
If using,say,a cooper's can with DME,then measure out half the DME (if multiple pounds are used) with a digital scale.
3) Make sure FV & anything that touches the beer is clean & sanitized.
4) When water boils (NO LID!),add the measured half of the DME,stiring to dissolve all clumps. There will be a mini hot break for a couple minutes. Unless you added wheat DME,then a big nasty one that'll need to be stirred down for 3 minutes or so.
5) Once that's done,Make you're hop additions. Keep the pot stirred up to where it's moving around all the time. I don't get scortching that way.
6) Once all hop additions are done & timer runs out,take the BK off the heat.
Add remaining DME,& all the can of LME. Rinse the can with some boiled water into the BK to get all the goodness. Stir the wort till no clumps of DME or no LME can be scraped off the bottom. Put a lid on the BK for 10-15 minutes so the heat can sanitize it.
7) Place the BK of wort in the sink,filling the empty spaces with ice,then top off with water. Use a thermometer to tell when the wort is chilled down to 65-70F. Put fermenter where it's going to sit,then place fine mesh strainer over the open fermenter & pour the wort & top off water through that. It'll aerate nicely,& strain out hops or grainy stuff at the same time. Stir the wort/top off water for 5 minutes solid to mix it well,& I mean stir roughly.
Take hydrometer sample,pitch yeast,seal & add airlock.
That's pretty much it for one way of brewing with both types of extract.