For culture, I usually dilute the patient's blood in different ratios (1:3, 1:5...) with fresh rbcs (obtained after a lymphoprep gradient) and cultured by Radfar et al method (Radfar et al Nature protocols 2009) without synchronization.
For parasite culture Marias answer should be sufficient. If you want to perform down stream analysis such proteomics or transcriptional analysis you may need to mature the parasites ex vivo in order to capture all the stages (rings, trophs and schizonts). They have unique profiles which you need to be aware of.
For short term in vitro P falciparum culture from the field collected blood what I do is given below-
I Collect 5 ml of Pf positive blood in 1 ml ACD in a 15 ml centrifuge tube. Centrifuge it at 3000 rpm for 10 minutes. Discard the supernatant (plasma) and wash the cell pellet 3 times with equal volume of IRPMI. Finally I add equal volume of CRPMI to make 50% HCT. Here I prepare a slide to assess the parasitaemia. Dilute it with 50% RBC (O+) to bring the parasitaemia level to 1% (one can keep 4-5% parasitaemia level, when starting the culture for the first time). I Make 6% HCT of this with CRPMI and take 4 ml of this in a 60 mm culture plate for initiating the culture. I Keep this petridish either in a CO2 incubator at 370C maintaining 5% CO2 or in a Candle jar maintaining 5% CO2/ CO2 incubator.
At least for Pf, you can 'isolate' the parasites from uninfected red blood cells and the contents of infected cells (ie, Hb), by use of sorbitol, leaving you just with parasites (and the ghosts of their host cells). You can also 'enrich' the infected red cells (ie, increase the parasitaemia) with Percoll or a magnet (eg, VarioMACS), but it sounds like it is probably the first method that you're after.